1000 (number)

"1,000", "Thousand", and "Chiliad" redirect here. For other uses, see 1000 (disambiguation) or, for the military unit, see Chiliarchy.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

← 999 1000 1001 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	one thousand
Ordinal	1000th (one thousandth)
Factorization	2^3 × 5^3
Divisors	1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Greek numeral	,Α´
Roman numeral	M
Roman numeral (unicode)	M, m, ↀ
Unicode symbol(s)	ↀ
Greek prefix	chilia
Latin prefix	milli
Binary	11111010002
Ternary	11010013
Senary	43446
Octal	17508
Duodecimal	6B412
Hexadecimal	3E816
Tamil	௲
Chinese	千
Punjabi	੧੦੦੦
Devanagari	१०००
Armenian	Ռ
Egyptian hieroglyph	𓆼

Look up thousand or 1000 in Wiktionary, the free dictionary.

A group of one thousand things is sometimes known, from Ancient Greek, as a chiliad.^[1] A period of one thousand years may be known as a chiliad or, more often from Latin, as a millennium. The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand.

Notation

• The decimal representation for one thousand is
  • 1000—a one followed by three zeros, in the general notation;
  • 1 × 10³—in engineering notation, which for this number coincides with:
  • 1 × 10³ exactly—in scientific normalized exponential notation;
  • 1 E+3 exactly—in scientific E notation.
• The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
• In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
• Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
• A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States, this is sometimes abbreviated with a "G" suffix.

Properties

1000 is the 10th icositetragonal number, or 24-gonal number.^[2] It is also the 16th generalized 30-gonal number.^[3]

1000 is the Wiener index of cycle length 20, also the sum of labeled boxes arranged as a pyramid with base 1 – 20.^[4][5][6][a]

1000 is the element of multiplicity in a ${\displaystyle 24\times 24}$  toroidal board in the n-Queens problem,^[8] with respective indicator of 25^[9] and count of 51.^[10][11]

1000 is the number of strict partitions of 50 containing the sum of no subset of the parts.^[12]

 

The regular polygram {1000/499} of the chiliagon, where its diagonals do not pass through the center, yet are closest to it (indistinguishably, unless one zooms in)

A chiliagon is a 1000-sided polygon,^[13][14] of order 2000 in its regular form.^[b]

Totient values

1000 has a reduced totient value ${\displaystyle \lambda (n)}$  of 100,^[20] and Euler totient ${\displaystyle \varphi (n)}$  of 400.^[16]

11 integers have a totient value of 1000 (1111, 1255, ..., 3750).^[16]

One thousand is also equal to the sum of Euler's totient summatory function ${\displaystyle \Phi (n)}$  over the first 57 integers.^[21]

Repdigits

In decimal, multiples of one thousand are totient values of four-digit repdigits:^[16]

• 7777 and 9999 have totients of 6000,
• 5555, and 8888 (as well as 11110) have totients of 4000,
• 3333, 4444 and 6666 have totients of 2000,
• 1111 and 2222 have a totient of 1000.

Notice, that in the list of composite numbers, 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number.^[22] Also,^[16]

• 5000 has a totient value of 2000, as does 5050 = 2025 + 3025 = 45² + 55², where
• 3000, 5000 and 7000 are the three multiples of one thousand, less than 10⁴, to not be totient values of four-digit repdigits;
• 10000 has a totient value of 4000. The totient of 1000 is 400, of 100 it is 40, and of 10 it is 4.

1600 = 40² is the totient value of 4000, as well as 6000, whose collective sum is 10000, where 6000 is the totient of 9999, one less than 10⁴.^[16][c]

The sum of the first nine prime numbers up to 23 is 100, with ${\displaystyle \varphi (p(23))=1000}$ , where ${\displaystyle p(23)=1255}$  is the number of integer partitions of 23.^[28]

Prime values

Using decimal representation as well,

• 997 is the 168th and largest prime number less than 1000,^[25] while
• 97 is the 25th and largest prime number less than 100; with
• 9 and 7 respectively the (4th) largest composite and prime less than 10.^[22][25]

On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973.^[25][d]

1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:^[37]

• 1,000,999
• 1,000,999,998,997
• 1,000,999,998,997,996,995,994,993

all represent prime numbers.^[38][39]

The one-thousandth prime number is 7919. It is a difference of 1 from the order of the smallest sporadic group: ${\displaystyle |\mathrm {M} _{11}|=7920}$ .^[40][41]

Numbers in the range 1001–1999

1001 to 1099

1001 = sphenic number (7 × 11 × 13), pentagonal number, pentatope number, palindromic number

1002 = sphenic number, Mertens function zero, abundant number, number of partitions of 22

1003 = the product of some prime p and the p^th prime, namely p = 17.

1004 = heptanacci number^[42]

1005 = Mertens function zero, decagonal pyramidal number^[43]

1006 = semiprime, product of two distinct isolated primes (2 and 503); unusual number; square-free number; number of compositions (ordered partitions) of 22 into squares; sum of two distinct pentatope numbers (5 and 1001); number of undirected Hamiltonian paths in 4 by 5 square grid graph;^[44] record gap between twin primes;^[45] number that is the sum of 7 positive 5th powers.^[46] In decimal: equidigital number; when turned around, the number looks like a prime, 9001; its cube can be concatenated from other cubes, 1_0_1_8_1_0_8_216 ("_" indicates concatenation, 0 = 0³, 1 = 1³, 8 = 2³, 216 = 6³)^[47]

1007 = number that is the sum of 8 positive 5th powers^[48]

1008 = divisible by the number of primes below it

1009 = smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (838₁₁, 474₁₅, 2F2₁₉, 1I1₂₄, 181₂₈). It is also a Lucky prime and Chen prime.

1010 = 10³ + 10,^[49] Mertens function zero

1011 = the largest n such that 2ⁿ contains 101 and does not contain 11011, Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction^[50]

1012 = ternary number, (32₁₀) quadruple triangular number (triangular number is 253),^[51] number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction^[50]

1013 = Sophie Germain prime,^[52] centered square number,^[53] Mertens function zero

1014 = 2¹⁰-10,^[54] Mertens function zero, sum of the nontriangular numbers between successive triangular numbers

1015 = square pyramidal number^[55]

1016 = member of the Mian–Chowla sequence,^[56] stella octangula number, number of surface points on a cube with edge-length 14^[57]

1017 = generalized triacontagonal number^[58]

1018 = Mertens function zero, 1018¹⁶ + 1 is prime^[59]

1019 = Sophie Germain prime,^[52] safe prime,^[60] Chen prime

1020 = polydivisible number

1021 = twin prime with 1019. It is also a Lucky prime.

1022 = Friedman number

1023 = sum of five consecutive primes (193 + 197 + 199 + 211 + 223);^[61] the number of three-dimensional polycubes with 7 cells;^[62] number of elements in a 9-simplex; highest number one can count to on one's fingers using binary; magic number used in Global Positioning System signals.

1024 = 32² = 4⁵ = 2¹⁰, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number.

1025 = Proth number 2¹⁰ + 1; member of Moser–de Bruijn sequence, because its base-4 representation (100001₄) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (4⁵ + 4⁰); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle

1026 = sum of two distinct powers of 2 (1024 + 2)

1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.

1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 2¹³.^[63]

1029 = can be written from base 2 to base 18 using only the digits 0 to 9.

1030 = generalized heptagonal number

1031 = exponent and number of ones for the fifth base-10 repunit prime,^[64] Sophie Germain prime,^[52] super-prime, Chen prime

1032 = sum of two distinct powers of 2 (1024 + 8)

1033 = emirp, twin prime with 1031

1034 = sum of 12 positive 9th powers^[65]

1035 = triangular number,^[66] hexagonal number^[67]

1036 = central polygonal number^[68]

1037 = number in E-toothpick sequence^[69]

1038 = even integer that is an unordered sum of two primes in exactly n ways^[70]

1039 = prime of the form 8n+7,^[71] number of partitions of 30 that do not contain 1 as a part,^[72] Chen prime

1040 = 4⁵ + 4²: sum of distinct powers of 4.^[73] The number of pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract.

1041 = sum of 11 positive 5th powers^[74]

1042 = sum of 12 positive 5th powers^[75]

1043 = number whose sum of even digits and sum of odd digits are even^[76]

1044 = sum of distinct powers of 4^[73]

1045 = octagonal number^[77]

1046 = coefficient of f(q) (3rd order mock theta function)^[78]

1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum^[79]

1048 = number of partitions of n into squarefree parts^[80]

1049 = Sophie Germain prime,^[52] highly cototient number,^[81] Chen prime

1050 = 1050₈ to decimal becomes a pronic number (552₁₀),^[82] number of parts in all partitions of 29 into distinct parts^[83]

1051 = centered pentagonal number,^[84] centered decagonal number

1052 = number that is the sum of 9 positive 6th powers^[85]

1053 = triangular matchstick number^[86]

1054 = centered triangular number^[87]

1055 = number that is the sum of 12 positive 6th powers^[88]

1056 = pronic number^[89]

1057 = central polygonal number^[90]

1058 = number that is the sum of 4 positive 5th powers,^[91] area of a square with diagonal 46^[92]

1059 = number n such that n⁴ is written in the form of a sum of four positive 4th powers^[93]

1060 = sum of the first 25 primes from 2 through 97 (the number of primes less than 100),^[94] and sixth sum of 10 consecutive primes, starting with 23 through 131.^[95]

1061 = emirp, twin prime with 1063, number of prime numbers having four digits^[96]

1062 = number that is not the sum of two palindromes^[97]

1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime^[98]

1064 = sum of two positive cubes^[99]

1065 = generalized duodecagonal^[100]

1066 = number whose sum of their divisors is a square^[101]

1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones^[102]

1068 = number that is the sum of 7 positive 5th powers,^[46] total number of parts in all partitions of 15^[103]

1069 = emirp^[104]

1070 = number that is the sum of 9 positive 5th powers^[105]

1071 = heptagonal number^[106]

1072 = centered heptagonal number^[107]

1073 = number that is the sum of 12 positive 5th powers^[75]

1074 = number that is not the sum of two palindromes^[97]

1075 = number non-sum of two palindromes^[97]

1076 = number of strict trees weight n^[108]

1077 = number where 7 outnumbers every other digit in the number^[109]

1078 = Euler transform of negative integers^[110]

1079 = every positive integer is the sum of at most 1079 tenth powers.

1080 = pentagonal number^[111]

1081 = triangular number,^[66] member of Padovan sequence^[112]

1082 = central polygonal number^[68]

1083 = three-quarter square,^[113] number of partitions of 53 into prime parts

1084 = third spoke of a hexagonal spiral,^[114] 1084⁶⁴ + 1 is prime

1085 = number of partitions of n into distinct parts > or = 2^[115]

1086 = Smith number,^[116] sum of totient function for first 59 integers

1087 = super-prime, cousin prime, lucky prime^[117]

1088 = octo-triangular number, (triangular number result being 136)^[118] sum of two distinct powers of 2, (1024 + 64)^[119] number that is divisible by exactly seven primes with the inclusion of multiplicity^[120]

1089 = 33², nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.^[121]

1090 = sum of 5 positive 5th powers^[122]

1091 = cousin prime and twin prime with 1093

1092 = divisible by the number of primes below it

1093 = the smallest Wieferich prime (the only other known Wieferich prime is 3511^[123]), twin prime with 1091 and star number^[124]

1094 = sum of 9 positive 5th powers,^[105] 1094⁶⁴ + 1 is prime

1095 = sum of 10 positive 5th powers,^[125] number that is not the sum of two palindromes

1096 = hendecagonal number,^[126] number of strict solid partitions of 18^[127]

1097 = emirp,^[104] Chen prime

1098 = multiple of 9 containing digit 9 in its base-10 representation^[128]

1099 = number where 9 outnumbers every other digit^[129]

1100 to 1199

1100 = number of partitions of 61 into distinct squarefree parts^[130]

1101 = pinwheel number^[131]

1102 = sum of totient function for first 60 integers

1103 = Sophie Germain prime,^[52] balanced prime^[132]

1104 = Keith number^[133]

1105 = 33² + 4² = 32² + 9² = 31² + 12² = 23² + 24², Carmichael number,^[134] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,^[135] centered square number,^[53] Fermat pseudoprime^[136]

1106 = number of regions into which the plane is divided when drawing 24 ellipses^[137]

1107 = number of non-isomorphic strict T₀ multiset partitions of weight 8^[138]

1108 = number k such that k⁶⁴ + 1 is prime

1109 = Friedlander-Iwaniec prime,^[139] Chen prime

1110 = k such that 2^k + 3 is prime^[140]

1111 = 11 × 101, palindrome that is a product of two palindromic primes,^[141] repunit^[142]

1112 = k such that 9^k - 2 is a prime^[143]

1113 = number of strict partions of 40^[144]

1114 = number of ways to write 22 as an orderless product of orderless sums^[145]

1115 = number of partitions of 27 into a prime number of parts^[146]

1116 = divisible by the number of primes below it

1117 = number of diagonally symmetric polyominoes with 16 cells,^[147] Chen prime

1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}^[148]

1119 = number of bipartite graphs with 9 nodes^[149]

1120 = number k such that k⁶⁴ + 1 is prime

1121 = number of squares between 34² and 34⁴.^[150]

1122 = pronic number,^[89] divisible by the number of primes below it

1123 = balanced prime^[132]

1124 = Leyland number^[151] = 2¹⁰ + 10², spy number

1125 = Achilles number

1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}^[152]

1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts^[153]

1128 = triangular number,^[66] hexagonal number,^[67] divisible by the number of primes below it

1129 = number of lattice points inside a circle of radius 19^[154]

1130 = skiponacci number^[155]

1131 = number of edges in the hexagonal triangle T(26)^[156]

1132 = number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs^[157]

1133 = number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}^[158]

1134 = divisible by the number of primes below it, triangular matchstick number^[86]

1135 = centered triangular number^[159]

1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph^[160]

1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid^[161]

1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138; particularly, a special code for Easter eggs on Star Wars DVDs.

1139 = wiener index of the windmill graph D(3,17)^[162]

1140 = tetrahedral number^[163]

1141 = 7-Knödel number^[164]

1142 = n such that n³² + 1 is prime,^[165] spy number

1143 = number of set partitions of 8 elements with 2 connectors^[166]

1144 is not the sum of a pair of twin primes^[167]

1145 = 5-Knödel number^[168]

1146 is not the sum of a pair of twin primes^[167]

1147 = 31 × 37 (a product of 2 successive primes)^[169]

1148 is not the sum of a pair of twin primes^[167]

1149 = a product of two palindromic primes^[170]

1150 = number of 11-iamonds without bilateral symmetry.^[171]

1151 = first prime following a prime gap of 22,^[172] Chen prime

1152 = highly totient number,^[173] 3-smooth number (2⁷×3²), area of a square with diagonal 48,^[92] Achilles number

1153 = super-prime, Proth prime^[174]

1154 = 2 × 24² + 2 = number of points on surface of tetrahedron with edgelength 24^[175]

1155 = number of edges in the join of two cycle graphs, both of order 33^[176]

1156 = 34², octahedral number,^[177] centered pentagonal number,^[84] centered hendecagonal number.^[178]

1157 = smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.^[179]

1158 = number of points on surface of octahedron with edgelength 17^[180]

1159 = member of the Mian–Chowla sequence,^[56] a centered octahedral number^[181]

1160 = octagonal number^[182]

1161 = sum of the first 26 primes

1162 = pentagonal number,^[111] sum of totient function for first 61 integers

1163 = smallest prime > 34².^[183] See Legendre's conjecture. Chen prime.

1164 = number of chains of multisets that partition a normal multiset of weight 8, where a multiset is normal if it spans an initial interval of positive integers^[184]

1165 = 5-Knödel number^[168]

1166 = heptagonal pyramidal number^[185]

1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43^[186]

1168 = antisigma(49)^[187]

1169 = highly cototient number^[81]

1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match

1171 = super-prime

1172 = number of subsets of first 14 integers that have a sum divisible by 14^[188]

1173 = number of simple triangulation on a plane with 9 nodes^[189]

1174 = number of widely totally strongly normal compositions of 16

1175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts^[153]

1176 = triangular number^[66]

1177 = heptagonal number^[106]

1178 = number of surface points on a cube with edge-length 15^[57]

1179 = number of different permanents of binary 7*7 matrices^[190]

1180 = smallest number of non-integral partitions into non-integral power >1000.^[191]

1181 = smallest k over 1000 such that 8*10^k-49 is prime.^[192]

1182 = number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)^[193]

1183 = pentagonal pyramidal number

1184 = amicable number with 1210^[194]

1185 = number of partitions of 45 into pairwise relatively prime parts^[195]

1186 = number of diagonally symmetric polyominoes with 15 cells,^[147] number of partitions of 54 into prime parts

1187 = safe prime,^[60] Stern prime,^[196] balanced prime,^[132] Chen prime

1188 = first 4 digit multiple of 18 to contain 18^[197]

1189 = number of squares between 35² and 35⁴.^[150]

1190 = pronic number,^[89] number of cards to build an 28-tier house of cards^[198]

1191 = 35² - 35 + 1 = H₃₅ (the 35th Hogben number)^[199]

1192 = sum of totient function for first 62 integers

1193 = a number such that 4¹¹⁹³ - 3¹¹⁹³ is prime, Chen prime

1194 =number of permutations that can be reached with 8 moves of 2 bishops and 1 rook on a 3 × 3 chessboard^[200]

1195 = smallest four digit number for which a⁻¹(n) is an integer is a(n) is 2*a(n-1) - (-1)^n[201]

1196 = ${\displaystyle \sum _{k=1}^{38}\sigma (k)}$ ^[202]

1197 = pinwheel number^[131]

1198 = centered heptagonal number^[107]

1199 = area of the 20th conjoined trapezoid^[203]

1200 to 1299

1200 = the long thousand, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages, the number of households the Nielsen ratings sample,^[204] number k such that k⁶⁴ + 1 is prime

1201 = centered square number,^[53] super-prime, centered decagonal number

1202 = number of regions the plane is divided into by 25 ellipses^[137]

1203: first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane^[205]

1204: magic constant of a 7 × 7 × 7 magic cube^[206]

1205 = number of partitions of 28 such that the number of odd parts is a part^[207]

1206 = 29-gonal number ^[208]

1207 = composite de Polignac number^[209]

1208 = number of strict chains of divisors starting with the superprimorial A006939(3)^[210]

1209 = The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*31

1210 = amicable number with 1184^[211]

1211 = composite de Polignac number^[209]

1212 = ${\displaystyle \sum _{k=0}^{17}p(k)}$ , where ${\displaystyle p}$  is the number of partions of ${\displaystyle k}$ ^[212]

1213 = emirp

1214 = sum of first 39 composite numbers,^[213] spy number

1215 = number of edges in the hexagonal triangle T(27)^[156]

1216 = nonagonal number^[214]

1217 = super-prime, Proth prime^[174]

1218 = triangular matchstick number^[86]

1219 = Mertens function zero, centered triangular number^[159]

1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons^[215]

1221 = product of the first two digit, and three digit repdigit

1222 = hexagonal pyramidal number

1223 = Sophie Germain prime,^[52] balanced prime, 200th prime number^[132]

1224 = number of edges in the join of two cycle graphs, both of order 34^[176]

1225 = 35², square triangular number,^[216] hexagonal number,^[67] centered octagonal number,^[217] icosienneagonal,^[218] hexacontagonal^[219] and hecatonicositetragonal (124-gonal).

1226 = number of rooted identity trees with 15 nodes ^[220]

1227 = smallest number representable as the sum of 3 triangular numbers in 27 ways^[221]

1228 = sum of totient function for first 63 integers

1229 = Sophie Germain prime,^[52] number of primes between 0 and 10000, emirp

1230 = the Mahonian number: T(9, 6)^[222]

1231 = smallest mountain emirp, as 121, smallest mountain number is 11 × 11

1232 = number of labeled ordered set of partitions of a 7-set into odd parts^[223]

1233 = 12² + 33²

1234 = number of parts in all partitions of 30 into distinct parts,^[83] smallest whole number containing all numbers from 1 to 4

1235 = excluding duplicates, contains the first four Fibonacci numbers ^[224]

1236 = 617 + 619: sum of twin prime pair^[225]

1237 = prime of the form 2p-1

1238 = number of partitions of 31 that do not contain 1 as a part^[72]

1239 = toothpick number in 3D^[226]

1240 = square pyramidal number^[55]

1241 = centered cube number,^[227] spy number

1242 = decagonal number^[135]

1243 = composite de Polignac number^[209]

1244 = number of complete partitions of 25^[228]

1245 = Number of labeled spanning intersecting set-systems on 5 vertices.^[229]

1246 = number of partitions of 38 such that no part occurs more than once^[230]

1247 = pentagonal number^[111]

1248 = the first four powers of 2 concatenated together

1249 = emirp, trimorphic number^[231]

1250 = area of a square with diagonal 50^[92]

1251 = 2 × 25² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25^[232]

1252 = 2 × 25² + 2 = number of points on surface of tetrahedron with edgelength 25^[175]

1253 = number of partitions of 23 with at least one distinct part^[233]

1254 = number of partitions of 23 into relatively prime parts^[234]

1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,^[145] number of partitions of 23^[235]

1256 = 1 × 2 × (5²)² + 6,^[236] Mertens function zero

1257 = number of lattice points inside a circle of radius 20^[154]

1258 = 1 × 2 × (5²)² + 8,^[236] Mertens function zero

1259 = highly cototient number^[81]

1260 = highly composite number,^[237] pronic number,^[89] the smallest vampire number,^[238] sum of totient function for first 64 integers, number of strict partions of 41^[144] and appears twice in the Book of Revelation

1261 = star number,^[124] Mertens function zero

1262 = maximal number of regions the plane is divided into by drawing 36 circles^[239]

1263 = rounded total surface area of a regular tetrahedron with edge length 27^[240]

1264 = sum of the first 27 primes

1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree^[241]

1266 = centered pentagonal number,^[84] Mertens function zero

1267 = 7-Knödel number^[164]

1268 = number of partitions of 37 into prime power parts^[242]

1269 = least number of triangles of the Spiral of Theodorus to complete 11 revolutions^[243]

1270 = 25 + 24×26 + 23×27,^[244] Mertens function zero

1271 = sum of first 40 composite numbers^[213]

1272 = sum of first 41 nonprimes^[245]

1273 = 19 × 67 = 19 × prime(19)^[246]

1274 = sum of the nontriangular numbers between successive triangular numbers

1275 = triangular number,^[66] sum of the first 50 natural numbers

1276 = number of irredundant sets in the 25-cocktail party graph^[247]

1277 = the start of a prime constellation of length 9 (a "prime nonuple")

1278 = number of Narayana's cows and calves after 20 years^[248]

1279 = Mertens function zero, Mersenne prime exponent

1280 = Mertens function zero, number of parts in all compositions of 9^[249]

1281 = octagonal number^[182]

1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts^[195]

1283 = safe prime^[60]

1284 = 641 + 643: sum of twin prime pair^[225]

1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.^[250]

1286 = number of inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree^[251]

1287 = ${\displaystyle {13 \choose 5}}$ ^[252]

1288 = heptagonal number^[106]

1289 = Sophie Germain prime,^[52] Mertens function zero

1290 = ${\displaystyle {\frac {1289+1291}{2}}}$ , average of a twin prime pair^[253]

1291 = largest prime < 6⁴,^[254] Mertens function zero

1292 = number such that phi(1292) = phi(sigma(1292)),^[255] Mertens function zero

1293 = ${\displaystyle \sum _{j=1}^{n}j\times prime(j)}$ ^[256]

1294 = rounded volume of a regular octahedron with edge length 14^[257]

1295 = number of edges in the join of two cycle graphs, both of order 35^[176]

1296 = 36² = 6⁴, sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard, also the maximum font size allowed in Adobe InDesign, number of combinations of 2 characters(00-ZZ)

1297 = super-prime, Mertens function zero, pinwheel number^[131]

1298 = number of partitions of 55 into prime parts

1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts^[258]

1300 to 1399

1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match; smallest even odd-factor hyperperfect number

1301 = centered square number,^[53] Honaker prime,^[259] number of trees with 13 unlabeled nodes^[260]

1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)^[156]

1303 = prime of form 21n+1 and 31n+1^[261][262]

1304 = sum of 1304₆ and 1304 ₉ which is 328+976

1305 = triangular matchstick number^[86]

1306 = Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 1¹ + 3² + 0³ + 6⁴. 135, 175, 518, and 598 also have this property. Centered triangular number.^[159]

1307 = safe prime^[60]

1308 = sum of totient function for first 65 integers

1309 = the first sphenic number followed by two consecutive such number

1310 = smallest number in the middle of a set of three sphenic numbers

1311 = number of integer partitions of 32 with no part dividing all the others^[263]

1312 = member of the Mian-Chowla sequence;^[56]

1313 = sum of all parts of all partitions of 14 ^[264]

1314 = number of integer partitions of 41 whose distinct parts are connected^[265]

1315 = 10^(2n+1)-7*10^n-1 is prime.^[266]

1316 = Euler transformation of sigma(11)^[267]

1317 = 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25^[268]

1318⁵¹² + 1 is prime,^[269] Mertens function zero

1319 = safe prime^[60]

1320 = 659 + 661: sum of twin prime pair^[225]

1321 = Friedlander-Iwaniec prime^[139]

1322 = area of the 21st conjoined trapezoid^[203]

1323 = Achilles number

1324 = if D(n) is the nth representation of 1, 2 arranged lexicographically. 1324 is the first non-1 number which is D(D(x))^[270]

1325 = Markov number,^[271] centered tetrahedral number^[272]

1326 = triangular number,^[66] hexagonal number,^[67] Mertens function zero

1327 = first prime followed by 33 consecutive composite numbers

1328 = sum of totient function for first 66 integers

1329 = Mertens function zero, sum of first 41 composite numbers^[213]

1330 = tetrahedral number,^[151] forms a Ruth–Aaron pair with 1331 under second definition

1331 = 11³, centered heptagonal number,^[107] forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form x² + x − 1, for x = 36.

1332 = pronic number^[89]

1333 = 37² - 37 + 1 = H₃₇ (the 37th Hogben number)^[199]

1334 = maximal number of regions the plane is divided into by drawing 37 circles^[239]

1335 = pentagonal number,^[111] Mertens function zero

1336 = sum of gcd(x, y) for 1 <= x, y <= 24,^[273] Mertens function zero

1337 = Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.

1338 = atomic number of the noble element of period 18,^[274] Mertens function zero

1339 = First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n^[275]

1340 = k such that 5 × 2^k - 1 is prime^[276]

1341 = First mountain number with 2 jumps of more than one.

1342 = ${\displaystyle \sum _{k=1}^{40}\sigma (k)}$ ,^[202] Mertens function zero

1343 = cropped hexagone^[277]

1344 = 37² - 5², the only way to express 1344 as a difference of prime squares^[278]

1345 = k such that k, k+1 and k+2 are products of two primes^[279]

1346= number of locally disjointed rooted trees with 10 nodes^[280]

1347 = concatenation of first 4 Lucas numbers ^[281]

1348 = number of ways to stack 22 pennies such that every penny is in a stack of one or two^[282]

1349 = Stern-Jacobsthal number^[283]

1350 = nonagonal number^[214]

1351 = number of partitions of 28 into a prime number of parts^[146]

1352 = number of surface points on a cube with edge-length 16,^[57] Achilles number

1353 = 2 × 26² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26^[232]

1354 = 2 × 26² + 2 = number of points on surface of tetrahedron with edgelength 26^[175]

1355 appears for the first time in the Recamán's sequence at n = 325,374,625,245.^[284] Or in other words A057167(1355) = 325,374,625,245^[285][286]

1356 is not the sum of a pair of twin primes^[167]

1357 = number of nonnegative solutions to x² + y² ≤ 41^2[287]

1358 = rounded total surface area of a regular tetrahedron with edge length 28^[240]

1359 is the 42d term of Flavius Josephus's sieve^[288]

1360 = 37² - 3², the only way to express 1360 as a difference of prime squares^[278]

1361 = first prime following a prime gap of 34,^[172] centered decagonal number, 3rd Mills' prime, Honaker prime^[259]

1362 = number of achiral integer partitions of 48^[289]

1363 = the number of ways to modify a circular arrangement of 14 objects by swapping one or more adjacent pairs^[290]

1364 = Lucas number^[291]

1365 = pentatope number^[292]

1366 = Arima number, after Yoriyuki Arima who in 1769 constructed this sequence as the number of moves of the outer ring in the optimal solution for the Chinese Rings puzzle^[293]

1367 = safe prime,^[60] balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),^[132]

1368 = number of edges in the join of two cycle graphs, both of order 36^[176]

1369 = 37², centered octagonal number^[217]

1370 = σ₂(37): sum of squares of divisors of 37^[294]

1371 = sum of the first 28 primes

1372 = Achilles number

1373 = number of lattice points inside a circle of radius 21^[154]

1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}^[148]

1375 = decagonal pyramidal number^[295]

1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^[296]

1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts^[153]

1378 = triangular number^[66]

1379 = magic constant of n × n normal magic square and n-queens problem for n = 14.

1380 = number of 8-step mappings with 4 inputs^[297]

1381 = centered pentagonal number^[84] Mertens function zero

1382 = first 4 digit tetrachi number ^[298]

1383 = 3 × 461. 10¹³⁸³ + 7 is prime^[299]

1384 = ${\displaystyle \sum _{k=1}^{41}\sigma (k)}$ ^[202]

1385 = up/down number^[300]

1386 = octagonal pyramidal number^[301]

1387 = 5th Fermat pseudoprime of base 2,^[302] 22nd centered hexagonal number and the 19th decagonal number,^[135] second Super-Poulet number.^[303]

1388 = 4 × 19² - 3 × 19 + 1 and is therefore on the x-axis of Ulams spiral^[304]

1389 = sum of first 42 composite numbers^[213]

1390 = sum of first 43 nonprimes^[245]

1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47^[186]

1392 = number of edges in the hexagonal triangle T(29)^[156]

1393 = 7-Knödel number^[164]

1394 = sum of totient function for first 67 integers

1395 = vampire number,^[238] member of the Mian–Chowla sequence^[56] triangular matchstick number^[86]

1396 = centered triangular number^[159]

1397 = ${\displaystyle \left\lfloor 5^{\frac {9}{2}}\right\rfloor }$ ^[305]

1398 = number of integer partitions of 40 whose distinct parts are connected^[265]

1399 = emirp^[306]

1400 to 1499

1400 = number of sum-free subsets of {1, ..., 15}^[307]

1401 = pinwheel number^[131]

1402 = number of integer partitions of 48 whose augmented differences are distinct,^[308] number of signed trees with 8 nodes^[309]

1403 = smallest x such that M(x) = 11, where M() is Mertens function^[310]

1404 = heptagonal number^[106]

1405 = 26² + 27², 7² + 8² + ... + 16², centered square number^[53]

1406 = pronic number,^[89] semi-meandric number^[311]

1407 = 38² - 38 + 1 = H₃₈ (the 38th Hogben number)^[199]

1408 = maximal number of regions the plane is divided into by drawing 38 circles^[239]

1409 = super-prime, Sophie Germain prime,^[52] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime^[174]

1410 = denominator of the 46th Bernoulli number^[312]

1411 = LS(41)^[313]

1412 = LS(42),^[313] spy number

1413 = LS(43)^[313]

1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations^[314]

1415 = the Mahonian number: T(8, 8)^[222]

1416 = LS(46)^[313]

1417 = number of partitions of 32 in which the number of parts divides 32^[315]

1418 = smallest x such that M(x) = 13, where M() is Mertens function^[310]

1419 = Zeisel number^[316]

1420 = Number of partitions of 56 into prime parts

1421 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 29-manifold to be realizable as a sub-manifold,^[317] spy number

1422 = number of partitions of 15 with two parts marked^[318]

1423 = 200 + 1223 and the 200th prime is 1223^[319] Also Used as a Hate symbol

1424 = number of nonnegative solutions to x² + y² ≤ 42^2[287]

1425 = self-descriptive number in base 5

1426 = sum of totient function for first 68 integers, pentagonal number,^[111] number of strict partions of 42^[144]

1427 = twin prime together with 1429^[320]

1428 = number of complete ternary trees with 6 internal nodes, or 18 edges^[321]

1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts^[258]

1430 = Catalan number^[322]

1431 = triangular number,^[66] hexagonal number^[67]

1432 = member of Padovan sequence^[112]

1433 = super-prime, Honaker prime,^[259] typical port used for remote connections to Microsoft SQL Server databases

1434 = rounded volume of a regular tetrahedron with edge length 23^[323]

1435 = vampire number;^[238] the standard railway gauge in millimetres, equivalent to 4 feet 8+1⁄2 inches (1.435 m)

1436 = discriminant of a totally real cubic field^[324]

1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^^[325]

1438 = k such that 5 × 2^k - 1 is prime^[276]

1439 = Sophie Germain prime,^[52] safe prime^[60]

1440 = a highly totient number^[173] and a 481-gonal number. Also, the number of minutes in one day, the blocksize of a standard 3+1/2 floppy disk, and the horizontal resolution of WXGA(II) computer displays

1441 = star number^[124]

1442 = number of parts in all partitions of 31 into distinct parts^[83]

1443 = the sum of the second trio of three-digit permutable primes in decimal: 337, 373, and 733. Also the number of edges in the join of two cycle graphs, both of order 37^[176]

1444 = 38², smallest pandigital number in Roman numerals

1445 = ${\displaystyle \sum _{k=0}^{3}\left({\binom {3}{k}}\times {\binom {3+k}{k}}\right)^{2}}$ ^[326]

1446 = number of points on surface of octahedron with edgelength 19^[180]

1447 = super-prime, happy number

1448 = number k such that phi(prime(k)) is a square^[327]

1449 = Stella octangula number

1450 = σ₂(34): sum of squares of divisors of 34^[294]

1451 = Sophie Germain prime^[52]

1452 = first Zagreb index of the complete graph K₁₂^[328]

1453 = Sexy prime with 1459

1454 = 3 × 22² + 2 = number of points on surface of square pyramid of side-length 22^[329]

1455 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1456 = number of regions in regular 15-gon with all diagonals drawn^[331]

1457 = 2 × 27² − 1 = a twin square^[332]

1458 = maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×3⁶)

1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime

1460 = The number of years that would have to pass in the Julian calendar in order to accrue a full year's worth of leap days.

1461 = number of partitions of 38 into prime power parts^[242]

1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices^[333]

1463 = total number of parts in all partitions of 16^[103]

1464 = rounded total surface area of a regular icosahedron with edge length 13^[334]

1465 = 5-Knödel number^[168]

1466 = ${\displaystyle \sum _{k=1}^{256}d(k)}$ , where ${\displaystyle d(k)}$  = number of divisors of ${\displaystyle k}$ ^[335]

1467 = number of partitions of 39 with zero crank^[336]

1468 = number of polyhexes with 11 cells that tile the plane by translation^[337]

1469 = octahedral number,^[177] highly cototient number^[81]

1470 = pentagonal pyramidal number,^[338] sum of totient function for first 69 integers

1471 = super-prime, centered heptagonal number^[107]

1472 = number of overpartitions of 15^[339]

1473 = cropped hexagone^[277]

1474 = ${\displaystyle {\frac {44(44+1)}{2}}+{\frac {44^{2}}{4}}}$ : triangular number plus quarter square (i.e., A000217(44) + A002620(44))^[340]

1475 = number of partitions of 33 into parts each of which is used a different number of times^[341]

1476 = coreful perfect number^[342]

1477 = 7-Knödel number^[164]

1478 = total number of largest parts in all compositions of 11^[343]

1479 = number of planar partitions of 12^[344]

1480 = sum of the first 29 primes

1481 = Sophie Germain prime^[52]

1482 = pronic number,^[89] number of unimodal compositions of 15 where the maximal part appears once^[345]

1483 = 39² - 39 + 1 = H₃₉ (the 39th Hogben number)^[199]

1484 = maximal number of regions the plane is divided into by drawing 39 circles^[239]

1485 = triangular number

1486 = number of strict solid partitions of 19^[127]

1487 = safe prime^[60]

1488 = triangular matchstick number^[86]

1489 = centered triangular number^[159]

1490 = tetranacci number^[346]

1491 = nonagonal number,^[214] Mertens function zero

1492 = discriminant of a totally real cubic field,^[324] Mertens function zero

1493 = Stern prime^[196]

1494 = sum of totient function for first 70 integers

1495 = 9###^[347]

1496 = square pyramidal number^[55]

1497 = skiponacci number^[155]

1498 = number of flat partitions of 41^[348]

1499 = Sophie Germain prime,^[52] super-prime

1500 to 1599

1500 = hypotenuse in three different Pythagorean triangles^[349]

1501 = centered pentagonal number^[84]

1502 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47^[350]

1503 = least number of triangles of the Spiral of Theodorus to complete 12 revolutions^[243]

1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^[296]

1505 = number of integer partitions of 41 with distinct differences between successive parts^[351]

1506 = number of Golomb partitions of 28^[352]

1507 = number of partitions of 32 that do not contain 1 as a part^[72]

1508 = heptagonal pyramidal number^[185]

1509 = pinwheel number^[131]

1510 = deficient number, odious number

1511 = Sophie Germain prime,^[52] balanced prime^[132]

1512 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1513 = centered square number^[53]

1514 = sum of first 44 composite numbers^[213]

1515 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 30-manifold to be realizable as a sub-manifold^[317]

1516 = ${\displaystyle \left\lfloor 9^{\frac {10}{3}}\right\rfloor }$ ^[353]

1517 = number of lattice points inside a circle of radius 22^[154]

1518 = sum of first 32 semiprimes,^[354] Mertens function zero

1519 = number of polyhexes with 8 cells,^[355] Mertens function zero

1520 = pentagonal number,^[111] Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition

1521 = 39², Mertens function zero, centered octagonal number,^[217] forms a Ruth–Aaron pair with 1520 under second definition

1522 = k such that 5 × 2^k - 1 is prime^[276]

1523 = super-prime, Mertens function zero, safe prime,^[60] member of the Mian–Chowla sequence^[56]

1524 = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1525 = heptagonal number,^[106] Mertens function zero

1526 = number of conjugacy classes in the alternating group A₂₇^[356]

1527 = number of 2-dimensional partitions of 11,^[357] Mertens function zero

1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21^[358]

1529 = composite de Polignac number^[209]

1530 = vampire number^[238]

1531 = prime number, centered decagonal number, Mertens function zero

1532 = number of series-parallel networks with 9 unlabeled edges,^[359] Mertens function zero

1533 = 21 × 73 = 21 × 21st prime^[246]

1534 = number of achiral integer partitions of 50^[289]

1535 = Thabit number

1536 = a common size of microplate, 3-smooth number (2⁹×3), number of threshold functions of exactly 4 variables^[360]

1537 = Keith number,^[133] Mertens function zero

1538 = number of surface points on a cube with edge-length 17^[57]

1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts^[153]

1540 = triangular number, hexagonal number,^[67] decagonal number,^[135] tetrahedral number^[151]

1541 = octagonal number^[182]

1542 = k such that 2^k starts with k^[361]

1543 = prime dividing all Fibonacci sequences,^[362] Mertens function zero

1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length^[363]

1545 = number of reversible string structures with 9 beads using exactly three different colors^[364]

1546 = number of 5 X 5 binary matrices with at most one 1 in each row and column,^[365] Mertens function zero

1547 = hexagonal pyramidal number

1548 = coreful perfect number^[342]

1549 = de Polignac prime^[366]

1550 = ${\displaystyle {\frac {31\times (3\times 31+7)}{2}}}$  = number of cards needed to build a 31-tier house of cards with a flat, one-card-wide roof^[367]

1551 = 6920 - 5369 = A169952(24) - A169952(23) = A169942(24) = number of Golomb rulers of length 24^[368][369]

1552 = Number of partitions of 57 into prime parts

1553 = 509 + 521 + 523 = a prime that is the sum of three consecutive primes^[370]

1554 = 2 × 3 × 7 × 37 = product of four distinct primes^[371]

1555² divides 6^1554[372]

1556 = sum of the squares of the first nine primes

1557 = number of graphs with 8 nodes and 13 edges^[373]

1558 = number k such that k⁶⁴ + 1 is prime

1559 = Sophie Germain prime^[52]

1560 = pronic number^[89]

1561 = a centered octahedral number,^[181] number of series-reduced trees with 19 nodes^[374]

1562 = maximal number of regions the plane is divided into by drawing 40 circles^[239]

1563 = ${\displaystyle \sum _{k=1}^{50}{\frac {50}{\gcd(50,k)}}}$ ^[375]

1564 = sum of totient function for first 71 integers

1565 = ${\displaystyle {\sqrt {1036^{2}+1173^{2}}}}$  and ${\displaystyle 1036+1173=47^{2}}$ ^[376]

1566 = number k such that k⁶⁴ + 1 is prime

1567 = number of partitions of 24 with at least one distinct part^[233]

1568 = Achilles number^[377]

1569 = 2 × 28² + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28^[232]

1570 = 2 × 28² + 2 = number of points on surface of tetrahedron with edgelength 28^[175]

1571 = Honaker prime^[259]

1572 = member of the Mian–Chowla sequence^[56]

1573 = discriminant of a totally real cubic field^[324]

1574²⁵⁶ + 1 is prime^[378]

1575 = odd abundant number,^[379] sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24^[235]

1576¹⁴ == 1 (mod 15^2)^[380]

1577 = sum of the quadratic residues of 83^[381]

1578 = sum of first 45 composite numbers^[213]

1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts^[258]

1580 = number of achiral integer partitions of 51^[289]

1581 = number of edges in the hexagonal triangle T(31)^[156]

1582 = a number such that the integer triangle [A070080(1582), A070081(1582), A070082(1582)] has an integer area^[382]

1583 = Sophie Germain prime

1584 = triangular matchstick number^[86]

1585 = Riordan number, centered triangular number^[159]

1586 = area of the 23rd conjoined trapezoid^[203]

1587 = 3 × 23² = number of edges of a complete tripartite graph of order 69, K_23,23,23^[383]

1588 = sum of totient function for first 72 integers

1589 = composite de Polignac number^[209]

1590 = rounded volume of a regular icosahedron with edge length 9^[384]

1591 = rounded volume of a regular octahedron with edge length 15^[257]

1592 = sum of all divisors of the first 36 odd numbers^[385]

1593 = sum of the first 30 primes

1594 = minimal cost of maximum height Huffman tree of size 17^[386]

1595 = number of non-isomorphic set-systems of weight 10

1596 = triangular number

1597 = Fibonacci prime,^[387] Markov prime,^[271] super-prime, emirp

1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}^[148]

1599 = number of edges in the join of two cycle graphs, both of order 39^[176]

1600 to 1699

1600 = 40², structured great rhombicosidodecahedral number,^[388] repdigit in base 7 (4444₇), street number on Pennsylvania Avenue of the White House, length in meters of a common High School Track Event, perfect score on SAT (except from 2005 to 2015)

1601 = Sophie Germain prime, Proth prime,^[174] the novel 1601 (Mark Twain)

1602 = number of points on surface of octahedron with edgelength 20^[180]

1603 = number of partitions of 27 with nonnegative rank^[389]

1604 = number of compositions of 22 into prime parts^[390]

1605 = number of polyominoes consisting of 7 regular octagons^[391]

1606 = enneagonal pyramidal number^[392]

1607 = member of prime triple with 1609 and 1613^[393]

1608 = ${\displaystyle \sum _{k=1}^{44}\sigma (k)}$ ^[202]

1609 = cropped hexagonal number^[277]

1610 = number of strict partions of 43^[144]

1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51^[186]

1612 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold^[317]

1613, 1607 and 1619 are all primes^[394]

1614 = number of ways of refining the partition 8^1 to get 1^8^[395]

1615 = composite number such that the square mean of its prime factors is a nonprime integer^[396]

1616 = ${\displaystyle {\frac {16(16^{2}+3\times 16-1)}{3}}}$  = number of monotonic triples (x,y,z) in {1,2,...,16}^3[397]

1617 = pentagonal number^[111]

1618 = centered heptagonal number^[107]

1619 = palindromic prime in binary, safe prime^[60]

1620 = 809 + 811: sum of twin prime pair^[225]

1621 = super-prime, pinwheel number^[131]

1622 = semiprime of the form prime + 1^[398]

1623 is not the sum of two triangular numbers and a fourth power^[399]

1624 = number of squares in the Aztec diamond of order 28^[400]

1625 = centered square number^[53]

1626 = centered pentagonal number^[84]

1627 = prime and 2 × 1627 - 1 = 3253 is also prime^[401]

1628 = centered pentagonal number^[84]

1629 = rounded volume of a regular tetrahedron with edge length 24^[323]

1630 = number k such that k^64 + 1 is prime

1631 = ${\displaystyle \sum _{k=0}^{5}(k+1)!{\binom {5}{k}}}$ ^[402]

1632 = number of acute triangles made from the vertices of a regular 18-polygon^[403]

1633 = star number^[124]

1634 = Narcissistic number in base 10

1635 = number of partitions of 56 whose reciprocal sum is an integer^[404]

1636 = number of nonnegative solutions to x² + y² ≤ 45^2[287]

1637 = prime island: least prime whose adjacent primes are exactly 30 apart^[405]

1638 = harmonic divisor number,^[406] 5 × 2¹⁶³⁸ - 1 is prime^[276]

1639 = nonagonal number^[214]

1640 = pronic number^[89]

1641 = 41² - 41 + 1 = H₄₁ (the 41st Hogben number)^[199]

1642 = maximal number of regions the plane is divided into by drawing 41 circles^[239]

1643 = sum of first 46 composite numbers^[213]

1644 = 821 + 823: sum of twin prime pair^[225]

1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection^[407]

1646 = number of graphs with 8 nodes and 14 edges^[373]

1647 and 1648 are both divisible by cubes^[408]

1648 = number of partitions of 34³ into distinct cubes^[409]

1649 = highly cototient number,^[81] Leyland number^[151]

1650 = number of cards to build an 33-tier house of cards^[198]

1651 = heptagonal number^[106]

1652 = number of partitions of 29 into a prime number of parts^[146]

1653 = triangular number, hexagonal number,^[67] number of lattice points inside a circle of radius 23^[154]

1654 = number of partitions of 42 into divisors of 42^[410]

1655 = rounded volume of a regular dodecahedron with edge length 6^[411]

1656 = 827 + 829: sum of twin prime pair^[225]

1657 = cuban prime,^[412] prime of the form 2p-1

1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations^[314]

1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52^[186]

1660 = sum of totient function for first 73 integers

1661 = 11 × 151, palindrome that is a product of two palindromic primes^[141]

1662 = number of partitions of 49 into pairwise relatively prime parts^[195]

1663 = a prime number and 5¹⁶⁶³ - 4¹⁶⁶³ is a 1163-digit prime number^[413]

1664 = k such that k, k+1 and k+2 are sums of 2 squares^[414]

1665 = centered tetrahedral number^[272]

1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)

1667 = 228 + 1439 and the 228th prime is 1439^[319]

1668 = number of partitions of 33 into parts all relatively prime to 33^[415]

1669 = super-prime, smallest prime with a gap of exactly 24 to the next prime^[416]

1670 = number of compositions of 12 such that at least two adjacent parts are equal^[417]

1671 divides the sum of the first 1671 composite numbers^[418]

1672 = 41² - 3², the only way to express 1672 as a difference of prime squares^[278]

1673 = RMS number^[419]

1674 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1675 = Kin number^[420]

1676 = number of partitions of 34 into parts each of which is used a different number of times^[341]

1677 = 41² - 2², the only way to express 1677 as a difference of prime squares^[278]

1678 = n such that n³² + 1 is prime^[165]

1679 = highly cototient number,^[81] semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts^[83]

1680 = highly composite number,^[237] number of edges in the join of two cycle graphs, both of order 40^[176]

1681 = 41², smallest number yielded by the formula n² + n + 41 that is not a prime; centered octagonal number^[217]

1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)

1683 = triangular matchstick number^[86]

1684 = centered triangular number^[159]

1685 = 5-Knödel number^[168]

1686 = ${\displaystyle \sum _{k=1}^{45}\sigma (k)}$ ^[202]

1687 = 7-Knödel number^[164]

1688 = number of finite connected sets of positive integers greater than one with least common multiple 72^[421]

1689 = ${\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}$ ^[422]

1690 = number of compositions of 14 into powers of 2^[423]

1691 = the same upside down, which makes it a strobogrammatic number^[424]

1692 = coreful perfect number^[342]

1693 = smallest prime > 41².^[183]

1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}^[148]

1695 = magic constant of n × n normal magic square and n-queens problem for n = 15. Number of partitions of 58 into prime parts

1696 = sum of totient function for first 74 integers

1697 = Friedlander-Iwaniec prime^[139]

1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree^[241]

1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree^[241]

1700 to 1799

1700 = σ₂(39): sum of squares of divisors of 39^[294]

1701 = ${\displaystyle \left\{{8 \atop 4}\right\}}$ , decagonal number, hull number of the U.S.S. Enterprise on Star Trek

1702 = palindromic in 3 consecutive bases: 898₁₄, 787₁₅, 6A6₁₆

1703 = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1^[425]

1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts^[426]

1705 = tribonacci number^[427]

1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4^[428]

1707 = number of partitions of 30 in which the number of parts divides 30^[315]

1708 = 2² × 7 × 61 a number whose product of prime indices 1 × 1 × 4 × 18 is divisible by its sum of prime factors 2 + 2 + 7 + 61^[429]

1709 = first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773

1710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts^[153]

1711 = triangular number, centered decagonal number

1712 = number of irredundant sets in the 29-cocktail party graph^[247]

1713 = number of aperiodic rooted trees with 12 nodes^[430]

1714 = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an 3 × 6 grid of squares^[431]

1715 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1716 = 857 + 859: sum of twin prime pair^[225]

1717 = pentagonal number^[111]

1718 = ${\displaystyle \sum _{d|12}{\binom {12}{d}}}$ ^[432]

1719 = composite de Polignac number^[209]

1720 = sum of the first 31 primes

1721 = twin prime; number of squares between 42² and 42⁴.^[150]

1722 = Giuga number,^[433] pronic number^[89]

1723 = super-prime

1724 = maximal number of regions the plane is divided into by drawing 42 circles^[239]

1725 = 47² - 22² = (prime(15))² - (nonprime(15))^2[434]

1726 = number of partitions of 44 into distinct and relatively prime parts^[435]

1727 = area of the 24th conjoined trapezoid^[203]

1728 = the quantity expressed as 1000 in duodecimal, that is, the cube of twelve (called a great gross), and so, the number of cubic inches in a cubic foot, palindromic in base 11 (1331₁₁) and 23 (363₂₃)

1729 = taxicab number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical Hair closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.

1730 = 3 × 24² + 2 = number of points on surface of square pyramid of side-length 24^[329]

1731 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1732 = ${\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}$ ^[436]

1733 = Sophie Germain prime, palindromic in bases 3, 18, 19.

1734 = surface area of a cube of edge length 17^[437]

1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts^[258]

1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18^[57]

1737 = pinwheel number^[131]

1738 = number of achiral integer partitions of 52^[289]

1739 = number of 1s in all partitions of 30 into odd parts^[438]

1740 = number of squares in the Aztec diamond of order 29^[400]

1741 = super-prime, centered square number^[53]

1742 = number of regions the plane is divided into by 30 ellipses^[137]

1743 = wiener index of the windmill graph D(3,21)^[162]

1744 = k such that k, k+1 and k+2 are sums of 2 squares^[414]

1745 = 5-Knödel number^[168]

1746 = number of unit-distance graphs on 8 nodes^[439]

1747 = balanced prime^[132]

1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55^[440]

1749 = number of integer partitions of 33 with no part dividing all the others^[263]

1750 = hypotenuse in three different Pythagorean triangles^[349]

1751 = cropped hexagone^[277]

1752 = 79² - 67², the only way to express 1752 as a difference of prime squares^[278]

1753 = balanced prime^[132]

1754 = k such that 5*2^k - 1 is prime^[276]

1755 = number of integer partitions of 50 whose augmented differences are distinct^[308]

1756 = centered pentagonal number^[84]

1757 = least number of triangles of the Spiral of Theodorus to complete 13 revolutions^[243]

1758 = ${\displaystyle \sum _{k=1}^{46}\sigma (k)}$ ^[202]

1759 = de Polignac prime^[366]

1760 = the number of yards in a mile

1761 = k such that k, k+1 and k+2 are products of two primes^[279]

1762 = number of binary sequences of length 12 and curling number 2^[441]

1763 = number of edges in the join of two cycle graphs, both of order 41^[176]

1764 = 42²

1765 = number of stacks, or planar partitions of 15^[442]

1766 = number of points on surface of octahedron with edgelength 21^[180]

1767 = σ(28²) = σ(35²)^[443]

1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation^[444]

1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts^[153]

1770 = triangular number, hexagonal number,^[67] Seventeen Seventy, town in Australia

1771 = tetrahedral number^[151]

1772 = centered heptagonal number,^[107] sum of totient function for first 76 integers

1773 = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively^[445]

1774 = number of rooted identity trees with 15 nodes and 5 leaves^[446]

1775 = ${\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}$ : sum of piles of first 10 primes^[447]

1776 = square star number.^[448] The number of pieces that could be seen in a 7 × 7 × 7× 7 Rubik's Tesseract.

1777 = smallest prime > 42².^[183]

1778 = least k >= 1 such that the remainder when 6^k is divided by k is 22^[449]

1779 = number of achiral integer partitions of 53^[289]

1780 = number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times^[450]

1781 = the first 1781 digits of e form a prime^[451]

1782 = heptagonal number^[106]

1783 = de Polignac prime^[366]

1784 = number of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that every pair of distinct elements has a different quotient^[452]

1785 = square pyramidal number,^[55] triangular matchstick number^[86]

1786 = centered triangular number^[159]

1787 = super-prime, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)

1788 = Euler transform of -1, -2, ..., -34^[453]

1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)^[454]

1790 = number of partitions of 50 into pairwise relatively prime parts^[195]

1791 = largest natural number that cannot be expressed as a sum of at most four hexagonal numbers.

1792 = Granville number

1793 = number of lattice points inside a circle of radius 24^[154]

1794 = nonagonal number,^[214] number of partitions of 33 that do not contain 1 as a part^[72]

1795 = number of heptagons with perimeter 38^[455]

1796 = k such that geometric mean of phi(k) and sigma(k) is an integer^[330]

1797 = number k such that phi(prime(k)) is a square^[327]

1798 = 2 × 29 × 31 = 10₂ × 11101₂ × 11111₂, which yield zero when the prime factors are xored together^[456]

1799 = 2 × 30² − 1 = a twin square^[332]

1800 to 1899

1800 = pentagonal pyramidal number,^[338] Achilles number, also, in da Ponte's Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally

1801 = cuban prime, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)^[412]

1802 = 2 × 30² + 2 = number of points on surface of tetrahedron with edgelength 30,^[175] number of partitions of 30 such that the number of odd parts is a part^[207]

1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)^[457]

1804 = number k such that k^64 + 1 is prime

1805 = number of squares between 43² and 43⁴.^[150]

1806 = pronic number,^[89] product of first four terms of Sylvester's sequence, primary pseudoperfect number,^[458] only number for which n equals the denominator of the nth Bernoulli number,^[459] Schröder number^[460]

1807 = fifth term of Sylvester's sequence^[461]

1808 = maximal number of regions the plane is divided into by drawing 43 circles^[239]

1809 = sum of first 17 super-primes^[462]

1810 = ${\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}$ ^[463]

1811 = Sophie Germain prime

1812 = n such that n³² + 1 is prime^[165]

1813 = number of polyominoes with 26 cells, symmetric about two orthogonal axes^[464]

1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six^[465]

1815 = polygonal chain number ${\displaystyle \#(P_{2,1}^{3})}$ ^[466]

1816 = number of strict partions of 44^[144]

1817 = total number of prime parts in all partitions of 20^[467]

1818 = n such that n³² + 1 is prime^[165]

1819 = sum of the first 32 primes, minus 32^[468]

1820 = pentagonal number,^[111] pentatope number,^[292] number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing^[469]

1821 = member of the Mian–Chowla sequence^[56]

1822 = number of integer partitions of 43 whose distinct parts are connected^[265]

1823 = super-prime, safe prime^[60]

1824 = 43² - 5², the only way to express 1824 as a difference of prime squares^[278]

1825 = octagonal number^[182]

1826 = decagonal pyramidal number^[295]

1827 = vampire number^[238]

1828 = meandric number, open meandric number, appears twice in the first 10 decimal digits of e

1829 = composite de Polignac number^[209]

1830 = triangular number

1831 = smallest prime with a gap of exactly 16 to next prime (1847)^[470]

1832 = sum of totient function for first 77 integers

1833 = number of atoms in a decahedron with 13 shells^[471]

1834 = octahedral number,^[177] sum of the cubes of the first five primes

1835 = absolute value of numerator of ${\displaystyle D_{6}^{(5)}}$ ^[472]

1836 = factor by which a proton is more massive than an electron

1837 = star number^[124]

1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}^[148]

1839 = ${\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }$ ^[473]

1840 = 43² - 3², the only way to express 1840 as a difference of prime squares^[278]

1841 = solution to the postage stamp problem with 3 denominations and 29 stamps,^[474] Mertens function zero

1842 = number of unlabeled rooted trees with 11 nodes^[475]

1843 = k such that phi(k) is a perfect cube,^[476] Mertens function zero

1844 = 3⁷ - 7³,^[477] Mertens function zero

1845 = number of partitions of 25 containing at least one prime,^[478] Mertens function zero

1846 = sum of first 49 composite numbers^[213]

1847 = super-prime

1848 = number of edges in the join of two cycle graphs, both of order 42^[176]

1849 = 43², palindromic in base 6 (= 12321₆), centered octagonal number^[217]

1850 = Number of partitions of 59 into prime parts

1851 = sum of the first 32 primes

1852 = number of quantales on 5 elements, up to isomorphism^[479]

1853 = sum of primitive roots of 27-th prime,^[480] Mertens function zero

1854 = number of permutations of 7 elements with no fixed points,^[481] Mertens function zero

1855 = rencontres number: number of permutations of [7] with exactly one fixed point^[482]

1856 = sum of totient function for first 78 integers

1857 = Mertens function zero, pinwheel number^[131]

1858 = number of 14-carbon alkanes C₁₄H₃₀ ignoring stereoisomers^[483]

1859 = composite de Polignac number^[209]

1860 = number of squares in the Aztec diamond of order 30^[484]

1861 = centered square number,^[53] Mertens function zero

1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition

1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition

1864 = Mertens function zero, ${\displaystyle {\frac {1864!-2}{2}}}$  is a prime^[485]

1865 = 12345₆: Largest senary metadrome (number with digits in strict ascending order in base 6)^[486]

1866 = Mertens function zero, number of plane partitions of 16 with at most two rows^[487]

1867 = prime de Polignac number^[366]

1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^^[325]

1869 = Hultman number: S_H(7, 4)^[488]

1870 = decagonal number^[135]

1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)^[489]

1872 = first Zagreb index of the complete graph K₁₃^[328]

1873 = number of Narayana's cows and calves after 21 years^[248]

1874 = area of the 25th conjoined trapezoid^[203]

1875 = 50² - 25²

1876 = number k such that k^64 + 1 is prime

1877 = number of partitions of 39 where 39 divides the product of the parts^[490]

1878 = n such that n³² + 1 is prime^[165]

1879 = a prime with square index^[491]

1880 = the 10th element of the self convolution of Lucas numbers^[492]

1881 = tricapped prism number^[493]

1882 = number of linearly separable Boolean functions in 4 variables^[494]

1883 = number of conjugacy classes in the alternating group A₂₈^[356]

1884 = k such that 5*2^k - 1 is prime^[276]

1885 = Zeisel number^[316]

1886 = number of partitions of 6⁴ into fourth powers^[495]

1887 = number of edges in the hexagonal triangle T(34)^[156]

1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^[296]

1889 = Sophie Germain prime, highly cototient number^[81]

1890 = triangular matchstick number^[86]

1891 = triangular number, hexagonal number,^[67] centered pentagonal number,^[84] centered triangular number^[159]

1892 = pronic number^[89]

1893 = 44² - 44 + 1 = H₄₄ (the 44th Hogben number)^[199]

1894 = maximal number of regions the plane is divided into by drawing 44 circles^[239]

1895 = Stern-Jacobsthal number^[283]

1896 = member of the Mian-Chowla sequence^[56]

1897 = member of Padovan sequence,^[112] number of triangle-free graphs on 9 vertices^[496]

1898 = smallest multiple of n whose digits sum to 26^[497]

1899 = cropped hexagone^[277]

1900 to 1999

1900 = number of primes <= 2¹⁴.^[63] Also 1900 (film) or Novecento, 1976 movie. 1900 was the year Thorold Gosset introduced his list of semiregular polytopes; it is also the year Max Brückner published his study of polyhedral models, including stellations of the icosahedron, such as the novel final stellation of the icosahedron.

1901 = Sophie Germain prime, centered decagonal number

1902 = number of symmetric plane partitions of 27^[498]

1903 = generalized catalan number^[499]

1904 = number of flat partitions of 43^[348]

1905 = Fermat pseudoprime^[136]

1906 = number n such that 3ⁿ - 8 is prime^[500]

1907 = safe prime,^[60] balanced prime^[132]

1908 = coreful perfect number^[342]

1909 = hyperperfect number^[501]

1910 = number of compositions of 13 having exactly one fixed point^[502]

1911 = heptagonal pyramidal number^[185]

1912 = size of 6th maximum raising after one blind in pot-limit poker^[503]

1913 = super-prime, Honaker prime^[259]

1914 = number of bipartite partitions of 12 white objects and 3 black ones^[504]

1915 = number of nonisomorphic semigroups of order 5^[505]

1916 = sum of first 50 composite numbers^[213]

1917 = number of partitions of 51 into pairwise relatively prime parts^[195]

1918 = heptagonal number^[106]

1919 = smallest number with reciprocal of period length 36 in base 10^[506]

1920 = sum of the nontriangular numbers between successive triangular numbers

1921 = 4-dimensional centered cube number^[507]

1922 = Area of a square with diagonal 62^[92]

1923 = 2 × 31² + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31^[232]

1924 = 2 × 31² + 2 = number of points on surface of tetrahedron with edgelength 31^[175]

1925 = number of ways to write 24 as an orderless product of orderless sums^[145]

1926 = pentagonal number^[111]

1927 = 2¹¹ - 11^2[508]

1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)^[509]

1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected^[265]

1930 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53^[350]

1931 = Sophie Germain prime

1932 = number of partitions of 40 into prime power parts^[242]

1933 = centered heptagonal number,^[107] Honaker prime^[259]

1934 = sum of totient function for first 79 integers

1935 = number of edges in the join of two cycle graphs, both of order 43^[176]

1936 = 44², 18-gonal number,^[510] 324-gonal number.

1937 = number of chiral n-ominoes in 12-space, one cell labeled^[511]

1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22^[180]

1939 = 7-Knödel number^[164]

1940 = the Mahonian number: T(8, 9)^[222]

1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines^[512]

1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes^[513]

1943 = largest number not the sum of distinct tetradecagonal numbers^[514]

1944 = 3-smooth number (2³×3⁵), Achilles number^[377]

1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime^[515]

1946 = number of surface points on a cube with edge-length 19^[57]

1947 = k such that 5·2^k + 1 is a prime factor of a Fermat number 2^2m + 1 for some m^[516]

1948 = number of strict solid partitions of 20^[127]

1949 = smallest prime > 44².^[183]

1950 = ${\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}$ ,^[517] largest number not the sum of distinct pentadecagonal numbers^[514]

1951 = cuban prime^[412]

1952 = number of covers of {1, 2, 3, 4}^[518]

1953 = triangular number

1954 = number of sum-free subsets of {1, ..., 16}^[307]

1955 = number of partitions of 25 with at least one distinct part^[233]

1956 = nonagonal number^[214]

1957 = ${\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}$  = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set^[519]

1958 = number of partitions of 25^[235]

1959 = Heptanacci-Lucas number^[520]

1960 = number of parts in all partitions of 33 into distinct parts^[83]

1961 = number of lattice points inside a circle of radius 25^[154]

1962 = number of edges in the join of the complete graph K₃₆ and the cycle graph C₃₆^[521]

1963! - 1 is prime^[522]

1964 = number of linear forests of planted planar trees with 8 nodes^[523]

1965 = total number of parts in all partitions of 17^[103]

1966 = sum of totient function for first 80 integers

1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem^[524]

σ(1968) = σ(1967) + σ(1966)^[525]

1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize^[526]

1970 = number of compositions of two types of 9 having no even parts^[527]

1971 = ${\displaystyle 3^{7}-6^{3}}$ ^[528]

1972 = n such that ${\displaystyle {\frac {n^{37}-1}{n-1}}}$  is prime^[529]

1973 = Sophie Germain prime, Leonardo prime

1974 = number of binary vectors of length 17 containing no singletons^[215]

1975 = number of partitions of 28 with nonnegative rank^[389]

1976 = octagonal number^[182]

1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons^[530]

1978 = n such that n | (3ⁿ + 5)^[531]

1979 = number of squares between 45² and 45⁴.^[150]

1980 = pronic number^[89]

1981 = pinwheel number^[131]

1982 = maximal number of regions the plane is divided into by drawing 45 circles^[239]

1983 = skiponacci number^[155]

1984 = 11111000000 in binary, see also: 1984 (disambiguation)

1985 = centered square number^[53]

1986 = number of ways to write 25 as an orderless product of orderless sums^[145]

1987 = 300th prime number

1988 = sum of the first 33 primes

1989 = number of 9-step mappings with 4 inputs^[297]

1990 = Stella octangula number

1991 = 11 × 181, the 46th Gullwing number,^[532] palindromic composite number with only palindromic prime factors^[533]

1992 = number of nonisomorphic sets of nonempty subsets of a 4-set^[534]

1993 = a number with the property that 4¹⁹⁹³ - 3¹⁹⁹³ is prime,^[535] number of partitions of 30 into a prime number of parts^[146]

1994 = Glaisher's function W(37)^[536]

1995 = number of unlabeled graphs on 9 vertices with independence number 6^[537]

1996 = a number with the property that (1996! + 3)/3 is prime^[538]

1997 = ${\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}$ ^[539]

1998 = triangular matchstick number^[86]

1999 = centered triangular number^[540] number of regular forms in a myriagram.

Prime numbers

There are 135 prime numbers between 1000 and 2000:^[541][542]

1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

Notes

1. 1000 is the fourth Wiener index of the grid ${\displaystyle P_{4}\times P_{4}}$  where ${\displaystyle P_{4}}$  is the path graph on four vertices.^[7] A connected graph with a given Wiener index represents the sum of the distances between all unordered pairs of vertices in said graph.
2. In the sequence of regular 1000-gonal numbers of the form ${\displaystyle n\times (499n-498)}$ , the first non-trivial solution is 2997.^[13] In Chowla's function, that counts the sum of divisors except for ${\displaystyle 1}$  and ${\displaystyle n}$ , 2997 is the first number to have a value of 1600,^[15] which is the Euler totient of 4000 and 6000,^[16] while the fifth member in the sequence 9985 (that follows 0, 1, 1000, 2997 and 5992)^[13] has an average of divisors that is 2997;^[17][18] with 5992 ÷ 2 = 2996, and 1000 + 2997 + 5992 = 9989 (a difference of 4 from the fourth member, after 1).
   There are 499 regular star polygrams to the regular chiliagon: 300 are regular compound star forms — a count that represents the twenty-fourth triangular number^[19] — with the remaining 199 forms represented by simple regular star polygons.
3. 1600, a repdigit in septenary (4444₇),^[23] is the composite index of 1891, in turn the like-index of 2223.^[22]
   2222 and 8888 are both numbers n such that n − 1 is prime (as with 4, 44, 444, and 888),^[24] yielding respectively the 331st and 1107th prime numbers,^[25] where the former (2221) is also the 64th super-prime.^[26] These two prime indexes collectively have a range of 777 integers (1107 : 331), which as a number is also a repdigit in senary.^[27]
4. The sum (2 + 3 + 5 + ... + 29) of the first 10 prime numbers is 129, which is the 97th indexed composite number.^[29][22] 9973 is also the 201st super-prime,^[26] where 1000 − 201 = 799, which is the smallest number in decimal to have a digit sum of 25,^[30] and the mirror permutation of digits of 997.
   When splitting four-digit 9973 into two two-digit numbers, 99 and 73, the latter is the composite index of 99, that, when added together is 172, the one hundred and thirty-second composite, with 132 itself the 99th composite;^[22] 73 is the twenty-first prime number.^[25]
   1601 is the 252nd prime,^[25] itself a value with a composite index of 197,^[22] where 1601 is the 40th and largest consecutive prime lucky number of Euler of the form n² + n + 41.^[31][32] The number of 4-digit prime numbers, in decimal, is its mirror permutation of digits 1061, the 172nd prime.^[33]
   Also, 7, 97 and 997 are all three respectively at a difference of 3 from 10, 100 and 1000, where, on the other hand, 9973 is 27 = 3³ away from 10000.
   8 as a binary number is "1000",^[34] and this representation, when written in factorial base, is equivalent to 24₁₀.^[35] In primorial base, it is equal to 30₁₀.^[36]

References

 

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1. "chiliad". Merriam-Webster. Archived from the original on 25 March 2022.
2. Sloane, N. J. A. (ed.). "Sequence A051876 (24-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 30 November 2022.
3. Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m equal to 0, +1, -1, +2, -2, +3, -3, ...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
4. Sloane, N. J. A. (ed.). "Sequence A034828 (a(n) equal to floor(n^2/4)*(n/2).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
5. Ngaokrajang, Kival. Sloane, N. J. A. (ed.). "Illustration for n equal to 1..10 [A034828]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Janjic, M.; Petkovic, B. (2013). "A Counting Function". pp. 14, 15. arXiv:1301.4550 [math.CO]. Bibcode:2013arXiv1301.4550J
7. Sloane, N. J. A. (ed.). "Sequence A143945 (Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
8. Sloane, N. J. A. (ed.). "Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
9. Sloane, N. J. A. (ed.). "Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
10. Sloane, N. J. A. (ed.). "Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
11. I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. doi:10.1080/00029890.1994.11997004 JSTOR 2974691
12. Sloane, N. J. A. (ed.). "Sequence A364349 (Number of strict integer partitions of n containing the sum of no subset of the parts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
13. Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers: a(n) equal to n*(499*n - 498).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
14. Aṣiru, Muniru A. (2016). "All square chiliagonal numbers". International Journal of Mathematical Education in Science and Technology. 47 (7). Oxfordshire: Taylor & Francis: 1123–1134. Bibcode:2016IJMES..47.1123A. doi:10.1080/0020739X.2016.1164346. MR 3528540. S2CID 123953958. Zbl 1396.97005.
15. Sloane, N. J. A. (ed.). "Sequence A048050 (Chowla's function: sum of divisors of n except for 1 and n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
16. Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and prime to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
17. Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 July 2023.
18. Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 July 2023.
19. Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
20. Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function psi(n): least k such that x^k is congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
21. Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function: a(n) is Sum_{k equal to1..n} phi(k), cf. A000010.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
22. Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
23. Sloane, N. J. A. (ed.). "Sequence A048332 (Numbers that are repdigits in base 7.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
24. Sloane, N. J. A. (ed.). "Sequence A028987 (Repdigit - 1 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
25. Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 19 December 2023.
26. Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 19 December 2023.
27. Sloane, N. J. A. (ed.). "Sequence A048331 (Numbers that are repdigits in base 6.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
28. Sloane, N. J. A. (ed.). "Sequence A366581 (a(n) equal to phi(p(n)), where phi is Euler's totient function (A000010) and p(n) is the number of partitions of n (A000041).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
29. Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
30. Sloane, N. J. A. (ed.). "Sequence A051885 (Smallest number whose sum of digits is n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20 December 2023.
31. Sloane, N. J. A. (ed.). "Sequence A202018 (a(n) equal to n^2 + n + 41.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
32. Sloane, N. J. A. (ed.). "Sequence A005846 (Primes of the form n^2 + n + 41.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
33. Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
34. Sloane, N. J. A. (ed.). "Sequence A007088 (The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
35. Sloane, N. J. A. (ed.). "Sequence A007623 (Integers written in factorial base.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
36. Sloane, N. J. A. (ed.). "Sequence A049345 (n written in primorial base.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
37. "1000". Prime Curious!. Archived from the original on 25 March 2022.
38. Sloane, N. J. A. (ed.). "Sequence A152396 (Let f(M,k) denote the decimal concatenation of k numbers starting with M: M | M-1 | M-2 | ... | M-k+1, k greater than 1. Then a(n) is the smallest M such that for all m in {1,..,n} an m-th prime occurs as f(M,k) for the smallest possible k, order prioritized m equal to 1 through n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
39. Sloane, N. J. A. (ed.). "Sequence A227949 (Primes obtained by concatenating decremented numbers starting at a power of 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
40. Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics. New York: Oxford University Press. pp. vii, 1–255. doi:10.1007/s00283-008-9007-9. ISBN 978-0-19-280722-9. MR 2215662. OCLC 180766312. Zbl 1113.00002.
41. Sloane, N. J. A. (ed.). "Sequence A001228 (Orders of sporadic simple groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
42. Sloane, N. J. A. (ed.). "Sequence A122189 (Heptanacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 13 July 2017.
43. Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
44. Sloane, N. J. A. (ed.). "Sequence A332307 (Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
45. Sloane, N. J. A. (ed.). "Sequence A036063 (Increasing gaps among twin primes: size)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
46. Sloane, N. J. A. (ed.). "Sequence A003352 (Numbers that are the sum of 7 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
47. Sloane, N. J. A. (ed.). "Sequence A061341 (A061341 Numbers not ending in 0 whose cubes are concatenations of other cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
48. Sloane, N. J. A. (ed.). "Sequence A003353 (Numbers that are the sum of 8 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
49. Sloane, N. J. A. (ed.). "Sequence A034262 (a(n) = n^3 + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
50. Sloane, N. J. A. (ed.). "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers < n+1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
51. Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers: a(n) = 2*n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
52. Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
53. Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
54. Sloane, N. J. A. (ed.). "Sequence A000325 (2^n - n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
55. Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
56. Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
57. Sloane, N. J. A. (ed.). "Sequence A005897 (6*n^2 + 2 for n > 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
58. Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
59. Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
60. Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes p: (p-1)/2 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
61. Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 1 November 2022.
62. Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 1 November 2022.
63. Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes < 2^n+1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
64. Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 25 February 2023.
65. Sloane, N. J. A. (ed.). "Sequence A004801 (Sum of 12 positive 9th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
66. Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
67. Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
68. Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
69. Sloane, N. J. A. (ed.). "Sequence A161328 (E-toothpick sequence (see Comments lines for definition))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
70. Sloane, N. J. A. (ed.). "Sequence A023036 (Smallest positive even integer that is an unordered sum of two primes in exactly n ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
71. Sloane, N. J. A. (ed.). "Sequence A007522 (Primes of the form 8n+7, that is, primes congruent to -1 mod 8)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
72. Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
73. Sloane, N. J. A. (ed.). "Sequence A000695 (Moser-de Bruijn sequence: sums of distinct powers of 4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
74. "A003356 - Oeis".
75. "A003357 - Oeis".
76. "A036301 - Oeis".
77. "A000567 - Oeis".
78. "A000025 - Oeis".
79. "A336130 - Oeis".
80. "A073576 - Oeis".
81. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 10 June 2016. Retrieved 12 June 2016.
82. "Base converter | number conversion".
83. Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
84. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 10 June 2016. Retrieved 12 June 2016.
85. "A003365 - Oeis".
86. Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
87. "A005448 - Oeis".
88. "A003368 - Oeis".
89. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 9 June 2016. Retrieved 12 June 2016.
90. "A002061 - Oeis".
91. "A003349 - Oeis".
92. Sloane, N. J. A. (ed.). "Sequence A001105 (2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
93. "A003294 - Oeis".
94. Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 February 2024.
95. Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 February 2024.
96. Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
97. "A035137 - Oeis".
98. "A347565: Primes p such that A241014(A000720(p)) is +1 or -1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 25 March 2022. Retrieved 19 January 2022.
99. "A003325 - Oeis".
100. "A195162 - Oeis".
101. "A006532 - Oeis".
102. "A341450 - Oeis".
103. Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
104. "A006567 - Oeis".
105. "A003354 - Oeis".
106. "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 11 June 2016. Retrieved 12 June 2016.
107. "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 9 June 2016. Retrieved 12 June 2016.
108. "A273873 - Oeis".
109. "A292457 - Oeis".
110. "A073592 - Oeis".
111. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 10 June 2016. Retrieved 12 June 2016.
112. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 10 June 2016. Retrieved 12 June 2016.
113. "A077043 - Oeis".
114. "A056107 - Oeis".
115. "A025147 - Oeis".
116. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 9 June 2016. Retrieved 12 June 2016.
117. "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 4 March 2016. Retrieved 12 June 2016.
118. "A033996 - Oeis".
119. "A018900 - Oeis".
120. "A046308 - Oeis".
121. "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 17 October 2015. Retrieved 14 June 2016.
122. "A003350 - Oeis".
123. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
124. "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. from the original on 11 June 2016. Retrieved 12 June 2016.
125. "A003355 - Oeis".
126. "A051682 - Oeis".
127. Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
128. "A121029 - Oeis".
129. "A292449 - Oeis".
130. Sloane, N. J. A. (ed.). "Sequence A087188 (number of partitions of n into distinct squarefree parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
131. Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
132. "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
133. "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
134. "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
135. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
136. Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
137. Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
138. Sloane, N. J. A. (ed.). "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
139. Sloane, N. J. A. (ed.). "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
140. Sloane, N. J. A. (ed.). "Sequence A057732 (Numbers k such that 2^k + 3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
141. Sloane, N. J. A. (ed.). "Sequence A046376 (Palindromes with exactly 2 palindromic prime factors (counted with multiplicity), and no other prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
142. "A002275 - OEIS". oeis.org. Retrieved 8 March 2024.
143. Sloane, N. J. A. (ed.). "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
144. Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
145. Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
146. Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
147. Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
148. Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
149. Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
150. Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
151. "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
152. Sloane, N. J. A. (ed.). "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
153. Sloane, N. J. A. (ed.). "Sequence A000096 (n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
154. Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
155. Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
156. Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
157. Sloane, N. J. A. (ed.). "Sequence A005380". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
158. Sloane, N. J. A. (ed.). "Sequence A051026 (Number of primitive subsequences of 1, 2, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
159. Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
160. Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
161. Sloane, N. J. A. (ed.). "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
162. Sloane, N. J. A. (ed.). "Sequence A033991 (n*(4*n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
163. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
164. Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
165. Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
166. Sloane, N. J. A. (ed.). "Sequence A185982 (Triangle read by rows: number of set partitions of n elements with k connectors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
167. Sloane, N. J. A. (ed.). "Sequence A007534 (Even numbers that are not the sum of a pair of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
168. Sloane, N. J. A. (ed.). "Sequence A050993 (5-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
169. Sloane, N. J. A. (ed.). "Sequence A006094 (Products of 2 successive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
170. Sloane, N. J. A. (ed.). "Sequence A046368 (Products of two palindromic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
171. "1150 (number)". The encyclopedia of numbers.
172. "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 July 2016.
173. "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
174. "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
175. Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
176. Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
177. "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
178. "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
179. "1157 (number)". The encyclopedia of numbers.
180. Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
181. Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
182. Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
183. Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
184. Sloane, N. J. A. (ed.). "Sequence A055887 (Number of ordered partitions of partitions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
185. Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
186. Sloane, N. J. A. (ed.). "Sequence A018805". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
187. Sloane, N. J. A. (ed.). "Sequence A024816 (Antisigma(n): Sum of the numbers less than n that do not divide n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
188. "A063776 - OEIS". oeis.org.
189. "A000256 - OEIS". oeis.org.
190. "1179 (number)". The encyclopedia of numbers.
191. "A000339 - OEIS". oeis.org.
192. "A271269 - OEIS". oeis.org.
193. "A000031 - OEIS". oeis.org.
194. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
195. Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

April 27, 2024