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# Annotated version of "What's Special About This Number?" (Part 1)

## Introduction

Erich Friedman has a very nice (and deservedly popular) page called
**What's Special About This Number?**

It does not, however, mention the sequences in the OEIS where these numbers can be found (and from where I suspect most of the entries were taken).

The present set of ten pages is a snapshot of his page as of May 23, 2010, with pointers to the corresponding entries in the OEIS. The pages are:

- Part 0: 0 to 999,
- Part 1: 1000 to 1999,
- Part 2: 2000 to 2999,
- Part 3: 3000 to 3999,
- Part 4: 4000 to 4999,
- Part 5: 5000 to 5999,
- Part 6: 6000 to 6999,
- Part 7: 7000 to 7999,
- Part 8: 8000 to 8999,
- Part 9: 9000 to 9999.

People are invited to add more pointers to these pages, by adding the appropriate A-numbers to the entries. It may be necessary to create new sequences to do this - see A158304 for an example.

To add a link to sequence A000108, for example, type A000108.

I should add that this is being done with Erich Friedman's approval.

I did not do a very good job of converting the original html format to wiki format, and in some cases you may have to refer to Erich's page to figure out the meaning or the links.

You may well find better descriptions for some numbers. If so, please send them to Erich and make the corresponding changes here. (The wiki software is complaining that these pages are too long. I decided to ignore these complaints.)

Neil Sloane

## Part 1: The Numbers 1000 to 1999

**1000** = 10^{3} (A011557)

**1001** is the smallest palindromic product of 3 consecutive primes (A169829)

**1002** is the number of partitions of 22 (A000041). 1002 also has the property that its base 2 expansion ends with its base 3 expansion (A169828)

**1003** has a base 2 representation that ends with its base 3 representation (A169828)

**1004** is a heptanacci number

**1005** is a decagonal pyramidal number

**1006** has a cube that is a concatenation of other cubes

**1007** is the maximum value of n so that there exist 8 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps

**1008** is the number of symmetric ways to fold a strip of 16 stamps

**1009** is the pseudosquare modulo 7

**1010** is the number of ways to tile a 5×12 rectangle with the pentominoes

**1011** has a square that is formed by inserting three 2's into it

**1012** has a square that is formed by inserting three 4's into it

**1013** is the number of ways 10 people can line up so that only one person has a taller person in front of him

**1014** is the smallest number that can be written in 7 ways as the sum of a number and the product of its non-zero digits

**1015** is the number of chiral invertible knots with 12 crossings

**1016** is a stella octangula number

**1019** is a value of n for which one more than the product of the first n primes is prime

**1020** is the number of ways to place 2 non-attacking kings on a 7×7 chessboard

**1021** is a value of n for which one more than the product of the first n primes is prime

**1022** is a Friedman number

**1023** is the smallest number with 4 different digits

**1024** is the smallest number with 11 divisors

**1025** is the smallest number that can be written as the sum of a square and a cube in 4 ways

**1026** is the number of subsets of the 22^{nd} roots of unity that add to 1

**1027** is the sum of the squares of the first 8 primes

**1029** is the smallest order for which there are 19 groups

**1031** is the length of the largest repunit that is known to be prime

**1032** is the smallest number that can be written as the sum of a cube and a 5^{th} power in more than one way

**1033** = 8^{1} + 8^{0} + 8^{3} + 8^{3}

**1035** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**1036** = 4444 in base 6

**1037** is a value of n for which φ (n) = φ (n-1) + φ (n-2)

**1038** is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies

**1040** is the number of the standard IRS tax form

**1041** does not occur in its factorial in base 2

**1042** has the property that if each digit is replaced by its cube , the resulting number is a cube

**1043** has a 5^{th} power that contains only digits 4 and smaller.

**1044** is the number of graphs with 7 vertices

**1045** is an octagonal pyramidal number (A002414)

**1046** is the smallest number whose cube contains 4 consecutive 4's

**1049** is an Eisenstein-Mersenne prime (A066408)

**1050** is the Stirling number of the second kind S(8,5)

**1051** is the smallest value of n for which π(8n) = n

**1052** has the property that placing the last digit first gives 1 more than twice it

**1053** divides the sum of the digits of 2^{1053} × 1053!

**1054** is a value of n for which |cos(n)| is smaller than any previous integer

**1055** is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 10 stamps

**1056** is the area of the smallest non-square rectangle that can be tiled with integer -sided squares

**1057** is the number of idempotent functions from a set of 6 elements into itself.

**1060** is the sum of the primes less than 100.

**1063** is not the sum of a square , a cube , a 4^{th} power, and a 5^{th} power

**1066** is a value of n for which 2φ (n) = φ (n+1)

**1067** has exactly the same digits in 3 different bases

**1069** is a prime that remains prime when preceded and followed by one, two, three, or four 3's

**1071** is the sum of 3 consecutive cubes

**1072** is the smallest number that can be written as the sum of 2, 3, 4, or 5 positive cubes

**1075** is the number of squares of functions from a set of 5 elements to itself

**1076** is a member of the Fibonacci -type sequence starting with 1 and 4

**1077** is a value of n for which n!!! + 1 is prime

**1078** is the number of lattices on 9 unlabeled nodes

**1079** is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 15

**1080** is the smallest number with 18 divisors

**1081** is a triangular number that is the product of two primes

**1084** is the smallest number whose English name contains all five vowels in order

**1086** is the number of 13-hexes with reflectional symmetry

**1087** is a Kynea prime

**1088** has a sum of digits equal to its largest prime factor

**1089** is one ninth of its reverse

**1092** is the order of a non-cyclic simple group

**1093** is the smallest Wieferich prime

**1094** is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 14 stamps

**1095** is the number of vertices in a Sierpinski triangle of order 6

**1096** is the number of subsets of {1,2,3,...,14} that have a sum divisible by 15

**1097** is the closest integer to e ^{7}

**1098** = 11 + 0 + 999 + 88

**1099** = 1 + 0 + 999 + 99

**1100** has a base 3 representation that ends with 1100

**1101** has a base 2 representation that ends with 1101

**1103** is the number of graphs with 9 vertices and 8 edges

**1104** is a Keith number

**1105** is the smallest number that can be written as the sum of 2 squares in 4 ways

**1107** is the 8^{th} central trinomial coefficient

**1110** is the sum of all numbers with digit sum 3 with 3 or fewer digits

**1111** is a repdigit

**1112** has a base 3 representation that begins with 1112

**1113** is the number of partitions of 40 into distinct parts

**1114** = 1^{2} + 2^{3} + 3^{4} + 4^{5}

**1116** is the number of 8-abolos

**1117** , when followed by any of its digits, is prime

**1118** is the number of graphs with 9 vertices that have chromatic number 2

**1119** is the number of bipartite graphs with 9 vertices

**1120** = (1 × 2 × 3 × 4 × 5 × 6 × 7 × 8) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8)

**1121** is the smallest number that can not be written using 12 copies of 12 and the operations +, –, ×, and ÷

**1122** = _{33}C _{1} + _{33}C _{1} + _{33}C _{2} + _{33}C _{2}

**1123** has digits which start the Fibonacci sequence

**1124** is a Leyland number

**1125** is a hendecagonal pyramidal number

**1127** has the property that if each digit is replaced by its square , the resulting number is a square

**1128** is an icosahedral number

**1130** is a Perrin number

**1131** has the property that the concatenation of its prime factors in increasing order is a square

**1132** is the number of 3-valent trees with 15 vertices

**1134** is the number of permutations of 9 items that fix 5 elements

**1135** is the number of ways to color the vertices of a triangle with 15 colors, up to rotation

**1137** is the maximum value of n so that there exist 7 denominations of stamps so that every postage from 1 to n can be paid for with at most 7 stamps

**1139** has the property that placing the last digit first gives 1 more than 8 times it

**1140** is the only number less than 10 million that can be written in 2 different ways as the sum of 3 or more consecutive numbers raised to consecutive powers

**1141** is the smallest number whose 6^{th} power can be written as the sum of seven 6^{th} powers

**1142** is the number of ways to place a non-attacking white and black pawn on a 7×7 chessboard

**1144** is the number of non-invertible knots with 12 crossings

**1146** divides the sum of the digits of 2^{1146} × 1146!

**1147** is the product of two consecutive primes

**1148** is the number of ways to fold a strip of 9 stamps

**1152** is a highly totient number

**1153** is the smallest number with the property that its first 3 multiples contain the digit 3

**1154** is the 8^{th} Pell-Lucas number

**1155** is the Stirling number of the second kind S(11,9)

**1156** is a square whose digits are non-decreasing

**1157** is the number of anisohedral 15-ominoes

**1158** is the maximum number of pieces a torus can be cut into with 18 cuts

**1159** is a centered octahedral number

**1160** is the maximum number of regions a cube can be cut into with 19 cuts

**1161** is the number of 11-iamonds without holes

**1165** is the number of conjugacy classes in the automorphism group of the 12 dimensional hypercube .

**1166** is a heptagonal pyramidal number

**1167** is the smallest number whose 8^{th} power can be written as the sum of nine 8^{th} powers

**1168** is the number of binary cube-free words of length 16

**1170** = 2222 in base 8

**1171** has a 4^{th} power containing only 4 different digits

**1172** is the number of subsets of {1,2,3,...,14} that have a sum divisible by 14

**1177** is a number whose sum of divisors is a 4^{th} power

**1179** is the number of different permanents of binary 7×7 matrices

**1182** is the number of necklaces (that can't be turned over) possible with 14 beads, each being one of 2 colors

**1183** is the smallest number with the property that its first 4 multiples contain the digit 3

**1184** is an amicable number

**1185** = 11 + 1111 + 8 + 55

**1186** is the number of 11-iamonds

**1187** = 111 + 111 + 888 + 77

**1188** is the number of triangles of any size contained in the triangle of side 16 on a triangular grid

**1189** is the square root of a triangular number

**1191** is the number of symmetric plane partitions of 25

**1192** is the number of 12-iamonds that do not tile the plane

**1193** and its reverse are prime , even if we append or prepend a 3 or 9

**1196** is the number of lines through exactly 2 points of a 9×9 grid of points

**1197** is the smallest number that contains as substrings the maximal prime powers that divide it

**1200** = 3333 in base 7

**1201** has a square that is formed by inserting three 4's into it

**1202** has the property that the concatenation of its prime factors in increasing order is a square

**1203** is the smallest number n for which the concatenation of n, (n+1), ... (n+34) is prime

**1206** is a Friedman number

**1207** is the product of two primes which are reverses of each other

**1209** = 1 × 3 × 13 × 31

**1210** is an amicable number

**1211** is the smallest number that ends an arithmetic progression of 9 numbers with the same prime signature

**1212** is the number of inequivalent asymmetric Ferrers graphs with 26 points

**1213** is the number of different degree sequences for graphs with 8 vertices

**1214** is a number whose product of digits is equal to its sum of digits

**1215** is the smallest number n where n and n+1 are both products of 6 or more primes

**1217** is a Proth prime

**1219** is a number whose sum of divisors is a 4^{th} power

**1220** is the number of labeled mappings from 5 points to themselves with exactly 2 cycles.

**1221** = 1 × 11 × 111

**1222** is a hexagonal pyramidal number

**1223** is the smallest number with complexity 24

**1224** is the smallest number that can be written as the sum of 4 cubes in 3 ways

**1225** is a hexagonal square triangular number

**1228** is a structured pentagonal hexacontahedral number

**1229** is the number of primes less than 10000 (A000720)

**1230** is the number of square-free graphs with 9 vertices

**1231** has the property that 1^{7} + 2^{7} + 3^{7} + 1^{7} = 1231_{8}

**1232** = (7 × 8 × 9 × 10 × 11) / (7 + 8 + 9 + 10 + 11)

**1233** = 12^{2} + 33^{2}

**1234** is the smallest 4-digit number with increasing digits

**1236** is the number of conjugacy classes of the alternating group A_{26}

**1238** is the number of rooted ternary trees with 11 vertices

**1239** is a value of n for which n^{8}, n^{9}, n^{10}, and n^{11} have the same digit sum

**1240** is the number of symmetric arrangements of 6 non-attacking queens on a 6×6 chessboard

**1241** is a centered cube number

**1243** is the number of essentially different ways to dissect a 18-gon into 8 quadrilaterals

**1245** is a dodecagonal pyramidal number

**1246** is the number of partitions of 38 in which no part occurs only once

**1248** is the smallest number with the property that its first 6 multiples contain the digit 4

**1249** is the number of simplicial polyhedra with 11 vertices

**1250** has a reciprocal that terminates in base 10

**1252** is the number of ways to tile a 4×24 rectangle with 4×1 rectangles

**1253** is a value of n for which σ (n+1) = 2σ (n)

**1254** is the number of 13-iamonds whose adjacency graph has a cycle

**1255** is a Friedman number

**1257** is a value of n for which φ (σ (n)) = φ (n)

**1260** is the smallest number with 36 divisors

**1261** is a Hexanacci -like number starting from 1, 1, 1, 1, 1, and 1

**1262** is the number of subsets of {1,2,3,...,14} that have a sum divisible by 13

**1265** has a 5^{th} power that contains the same digits as 164^{7}

**1271** has a 6^{th} power whose last few digits are ...21211121

**1275** is the smallest number so that it and its neighbors are products of two primes and the square of a prime

**1276** = 1111 + 22 + 77 + 66

**1278** has a square root whose decimal part starts with the digits 1-9 in some order

**1279** is the exponent of a Mersenne prime (A000043, A000668)

**1280** is the number of tilted rectangles with vertices in a 10×10 grid

**1281** has the property that if each digit is replaced by its square , the resulting number is a square

**1283** is the number of ways to divide a 8×8 grid of points into two sets using a straight line

**1285** is the number of 9-ominoes

**1287** = _{13}C _{5}

**1288** is the number of possible positions in Othello after 2.5 moves

**1289** is a truncated octahedral number

**1291** is the number of possible rows in a 16×16 crossword puzzle

**1292** is a factor of the sum of the digits of 1292^{1292}

**1293** is a structured truncated tetrahedral number

**1294** is the number of 4 dimensional polytopes with 8 vertices

**1295** = 5555 in base 6

**1296** is a Friedman number

**1297** is a Tetranacci -like number starting from 1, 1, 1, and 1

**1298** has a base 3 representation that ends with its base 6 representation

**1299** are the first 4 digits of 8^{1299}

**1300** is the sum of the first four 5^{th} powers

**1301** is the number of trees with 13 vertices

**1302** is the number of trees on 17 vertices with diameter 5

**1303** is the number of multigraphs with 7 vertices and 8 edges

**1304** = 1304_{6} + 1304_{9}

**1305** is the number of graphs with 11 vertices and 9 edges

**1306** = 1^{1} + 3^{2} + 0^{3} + 6^{4}

**1307** is a number n for which n^{2}+1 is 7 times another square

**1308** is the smallest value of n for which n, n+1, n+2, and n+3 have the same number of prime factors

**1309** is a member of the Fibonacci -type sequence starting with 1 and 5

**1310** is the smallest number so that it and its neighbors are products of three distinct primes

**1311** is the trinomial coefficient T(19,16)

**1314** divides the sum of the digits of 1314!

**1318** is the rectilinear crossing number of complete graph K_{19}

**1320** = _{12}P _{3}

**1323** is an Achilles number

**1324** is the Entringer number E(7,5).

**1325** is a Markov number

**1327** is the smallest prime for which the closest 6 primes are all smaller

**1328** and the following 32 numbers are composite

**1330** = _{21}C _{3}

**1331** is a cube containing only odd digits

**1332** has a base 2 representation that begins and ends with its base 6 representation

**1333** has a base 2 representation that ends with its base 6 representation

**1334** is a value of n for which σ (n) = σ (n+1)

**1337** spells Leet in Leet

**1340** has a square with a digit sum larger than its 5^{th} power

**1344** is the order of a perfect group (A060793)

**1348** is the number of ways to stack 22 pennies in contiguous rows so that each penny lies on the table or on two pennies

**1349** is the maximum number of pieces a torus can be cut into with 19 cuts

**1351** has the property that e ^{1351] } is within .0009 of an integer

**1352** is an hexagonal prism number

**1353** is the ratio of Fibonacci numbers

**1354** has a 5^{th} power that is closer to a cube than a square

**1356** is a truncated square pyramid number

**1357** has digits in arithmetic sequence

**1360** is the number of ways to place 3 non-attacking knights on a 5×5 chessboard

**1361** is the index of a prime Lucas number

**1362** is the smallest number that has a square root whose decimal part starts with the digits 0-9 in some order

**1363** is a value of n for which σ (φ (n)) = 2σ (n)

**1364** is the 15^{th} Lucas number

**1365** = _{15}C _{4}

**1366** is the number of ways to place 28 points on a 14×14 grid so that no 3 points are on a line

**1367** is the number of anisohedral 18-iamonds

**1368** is the number of ways to fold a 3×3 rectangle of stamps

**1369** is a square whose digits are non-decreasing

**1370** = 1^{2} + 37^{2} + 0^{2}

**1371** = 1^{2} + 37^{2} + 1^{2}

**1372** is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 10

**1373** is the number of digits of the 17^{th} perfect number (A061193)

**1375** is a decagonal pyramidal number

**1376** is the smallest number with the property that it and its neighbors are not cubefree

**1377** is the number of interior intersections when all the diagonals of a regular 16-gon are drawn

**1378** is the number of symmetric idempotent 6×6 matrices over GF(2)

**1379** is the magic constant of a 24×24 magic square

**1380** is the number of intersections when all the diagonals of a regular 15-gon are drawn

**1381** is the number of anisohedral 17-ominoes

**1383** is the number of anisohedral 13-hexes

**1384** has the same digits as the 1384^{th} prime

**1385** is the 4^{th} secant number

**1386** = 1 + 3^{4} + 8 + 6^{4}

**1387** divides the sum of the binary digits of 1387!

**1390** is the smallest number in base 6 to have 5 different digits

**1391** is the number of squares in a 10×10 grid of squares with diagonals drawn

**1392** is the number of ternary square-free words of length 18

**1393** is an NSW number

**1394** is the maximum number of regions space can be divided into by 17 spheres

**1395** is a vampire number

**1399** is the number of subsets of {1,2,3,...,13} that have an integer average

**1400** is the number of different arrangements of 4 non-attacking queens on a 4×10 chessboard

**1405** is the sum of consecutive squares in 2 ways

**1406** has a 4^{th} root that starts 6.12345...

**1408** is the number of symmetric 3×3 matrices in base 4 with determinant 0

**1409** is the only positive number known whose 8^{th} power can be written as the sum of eight 8^{th} powers

**1410** is the number of Ore graphs with 9 vertices

**1411** is the number of quasi-groups of order 5

**1412** has a cube whose digits occur with the same frequency

**1413** is the smallest number that can not be formed using the digits 0-7 at most once, together with the symbols + – × and ÷

**1414** is the smallest number whose square contains 3 consecutive 9's

**1415** is a centered icosahedral number

**1416** is the number of connected planar maps with 6 edges

**1419** is a Zeisel number

**1421** is a value of n for which σ (φ (n)) = 2σ (n)

**1422** is the number of ways to stack 27 boxes in a line so that each box lies on the table or on a box next to 2 boxes

**1423** is the number of digits in the 3^{rd} Cullen prime

**1426** is the number of partitions of 42 into distinct parts

**1427** is the number of ways to write 23 as the ordered sum of positive squares

**1428** is the number of ways a 6×1 rectangle can be surrounded by 6×1 rectangles

**1429** is the smallest number whose square has the first 3 digits the same as the next 3 digits

**1430** is the 8^{th} Catalan number

**1432** is a Padovan number

**1434** is a number whose sum of squares of the divisors is a square

**1435** is a vampire number

**1437** is the smallest number that can not be formed using the digit 1 at most 19 times, together with the symbols +, × and ^

**1438** is the smallest number with complexity 25

**1439** is the smallest number with complexity 26

**1440** = 2! × 3! × 5!

**1441** is a palindrome in base 6 and in base 10

**1443** is a number n for which the sum of the first n composite numbers is a palindrome

**1444** is a square whose digits are non-decreasing

**1445** divides the sum of the binary digits of 1445!

**1446** is the number of graphs with 9 vertices and 5 edges

**1448** is the number of 8-hexes

**1449** is a stella octangula number

**1452** is a value of n so that n(n+4) is a palindrome

**1453** is a member of the Fibonacci -type sequence starting with 2 and 5

**1454** = 11 + 444 + 555 + 444

**1455** is the number of subgroups of the symmetric group on 6 symbols

**1456** is the number of regions formed when all diagonals are drawn in a regular 15-gon

**1457** is a number that does not have any digits in common with its cube

**1458** is the maximum determinant of a binary 11×11 matrix

**1459** is the sum of the cubes of the digits of the sum of the cubes of its digits

**1460** is a value of n for which n^{2} and n^{3} use the same digits

**1464** = 1111 in base 11

**1465** has a square that is formed by inserting three 2's into it

**1467** has the property that e ^{π √1467} is within 10^{-8} of an integer

**1468** is the smallest number whose 6^{th} power has 20 digits

**1469** is the number of ways to play the first 4 moves in Checkers

**1470** is a pentagonal pyramidal number

**1471** is the number of regions the complex plane is cut into by drawing lines between all pairs of 15^{th} roots of unity

**1474** is a member of the Fibonacci -type sequence starting with 2 and 9

**1475** is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 11 stamps

**1476** is the number of graphs with 9 edges

**1477** is a value of n for which n! + 1 is prime

**1479** is the number of planar partitions of 12

**1480** is the number of asymmetric trees with 19 vertices

**1481** is a number n for which n, n+2, n+6, and n+8 are all prime

**1485** is the number of 3-colored rooted trees with 5 vertices

**1486** is the number of different score sequences of an 10-team round robin tournament]

**1490** is the 14^{th} Tetranacci number

**1491** has an 8^{th} power whose first few digits are 24424244...

**1493** is the largest known Stern prime

**1494** is the sum of its proper divisors that contain the digit 4

**1496** is the sum of the first 16 squares

**1497** is a Perrin number

**1498** is the number of inequivalent asymmetric Ferrers graphs with 27 points

**1499** is a prime that remains prime if any digit is deleted

**1500** = (5+1) × (5+5) × (5+0) × (5+0)

**1503** is a Friedman number

**1504** is the number of anisohedral 21-iamonds

**1505** is the number of necklaces possible with 6 beads, each being one of 5 colors

**1506** is the sum of its proper divisors that contain the digit 5

**1508** is a heptagonal pyramidal number

**1512** is the number of inequivalent Ferrers graphs with 27 points

**1514** is a number whose square and cube use different digits

**1515** is the number of trees on 15 vertices with diameter 6

**1517** is the product of two consecutive primes

**1518** is the sum of its proper divisors that contain the digit 5

**1520** is the smaller number in a Ruth-Aaron pair

**1521** is the smallest number that can be written as the sum of 4 distinct cubes in 3 ways

**1522** has the property that if each digit is replaced by its square , the resulting number is a square

**1525** is a value of n for which σ (φ (n)) = 2σ (n)

**1526** is the number of conjugacy classes of the alternating group A_{27}

**1530** is a vampire number

**1531** appears inside its 4^{th} power

**1532** is the number of series-parallel networks with 9 unlabeled edges

**1533** is a Kaprekar constant in base 2

**1534** = 4321 in base 7

**1536** is not the sum of 4 non-zero squares

**1537** has the property that dropping its first and last digits gives its largest prime factor

**1538** does not occur in its factorial in base 2

**1540** is a tetrahedal triangular number

**1541** is a value of n for which φ (n) = φ (n-1) + φ (n-2)

**1542** are the first 4 digits of 2^{1542}

**1543** = 1111 + 55 + 44 + 333

**1544** is the number of connected 4-regular graphs with 12 vertices

**1545** is a cubic star number

**1547** is a hexagonal pyramidal number

**1549** is the smallest mutli-digit number that is not the sum of a prime and a non-trivial power

**1552** has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers

**1553** is the number of polygons formed by 9 points on a circle, if adjacent points can not be joined

**1554** is the trinomial coefficient T(9,3)

**1555** is the largest n so that **Q** (√n) has class number 4

**1556** is the sum of the squares . of the first 9 primes

**1557** has a square where the first 6 digits alternate

**1559** is the smallest prime p with 16 consecutive quadratic residues mod p

**1560** is the maximum number of pieces a torus can be cut into with 20 cuts

**1561** is the number of series-reduced trees with 19 vertices

**1562** = 22222 in base 5

**1563** is the smallest number with the property that its first 4 multiples contain the digit 6

**1568** is the smallest Rhonda number

**1569** is the number of labeled mappings from 5 points to themselves with exactly 1 cycles.

**1571** is the smallest number that can not be formed using the digit 1 at most 23 times, together with the symbols +, –, × and ÷

**1573** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**1574** is the closest integer to 15^{e }

**1575** is the number of partitions of 24

**1577** divides 1^{1} + 2^{2} + 3^{3} + ^{ . . .} + 1577^{1577}

**1578** is the number of Hamiltonian paths of a 3×8 rectangle graph

**1579** is the smallest prime that remains prime when preceded and followed by one, two, three, or four 9's

**1581** is the smallest number whose 8^{th} power contains exactly the same digits as another 8^{th} power

**1582** is a value of n so that n(n+4) is a palindrome

**1584** has a base 3 representation that ends with its base 6 representation

**1585** has a base 3 representation that ends with its base 6 representation

**1586** has a base 3 representation that ends with its base 6 representation

**1587** is a number that does not have any digits in common with its cube

**1589** is the starting location of 7777 in the decimal expansion of π

**1591** is the sum of the first 13 numbers that have digit sum 13

**1592** is a number that does not have any digits in common with its cube

**1593** has the property that dropping its first and last digits gives its largest prime factor

**1595** is the smallest quasi-Carmichael number in base 2

**1596** is the sum of the first 15 Fibonacci numbers

**1597** is the 17^{th} Fibonacci number

**1600** = 4444 in base 7

**1601** is the number of forests with 12 vertices

**1605** is the number of 7-octs

**1606** is the number of strongly connected digraphs with 4 vertices

**1609** is the smallest number whose square contains 4 consecutive 8's

**1610** is the number of partitions of 43 into distinct parts

**1613** is the index of a prime Euclid number

**1614** is the number of arrangements of 5 non-attacking queens on a 9×5 chessboard

**1617** is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 9 stamps

**1618** has the property that the concatenation of its prime factors in increasing order is a square

**1620** is a highly abundant number (A002093)

**1621** is a prime that remains prime when preceded and followed by one, two, three, or four 3's

**1624** is the Stirling number of the first kind s(7,3)

**1626** is the number of binary partitions of 31

**1627** is the smallest prime so that it and the next 2 primes all end in 7

**1629** is an icosahedral number

**1630** is the number of 14-ominoes with a line of symmetry

**1632** is the smallest number with the property that its first 5 multiples contain the digit 6

**1633** is a number whose square and cube use different digits

**1634** is a narcissistic number

**1635** has a 5^{th} root whose decimal part starts with the digits 1-9 in some order

**1636** appears inside its 4^{th} power

**1637** is the number of graphs with 9 vertices and 10 edges

**1638** is a harmonic divisor number

**1639** is the number of binary rooted trees with 16 vertices

**1640** = 2222 in base 9

**1641** has the property that if each digit is replaced by its square , the resulting number is a square

**1643** = 31 × 53 = 3153_{8}

**1648** is a betrothed number

**1649** is a Leyland number

**1650** is the number of connected partial orders on 7 unlabeled elements

**1651** is the trinomial coefficient T(13,9)

**1652** is a member of the Fibonacci -type sequence starting with 4 and 9

**1657** is a Cuban prime

**1659** is a structured truncated octahedral number

**1661** is a centered dodecahedral number

**1663** is the number of partitions of 41 in which no part occurs only once

**1664** is a value of n so that n(n+9) is a palindrome

**1665** is the number of triangles of any size contained in the triangle of side 18 on a triangular grid

**1666** is the sum of the Roman numerals

**1667** + φ (1667) = 3333

**1668** is the maximum number of regions space can be divided into by 18 spheres

**1669** is the smallest number whose 9^{th} power has 29 digits

**1670** has a 6^{th} root that starts 3.44444...

**1671** divides the sum of the first 681 composite numbers

**1673** is a number whose sum of squares of the divisors is a square

**1674** is the smallest n for which Σ_{k≤n} 1/k ≥ 8

**1675** has the property that dropping its first and last digits gives its largest prime factor

**1676** = 1^{1} + 6^{2} + 7^{3} + 6^{4}

**1679** is the smallest multiple of 23 whose digits add to 23

**1680** is the smallest number with 40 divisors

**1681** is a square and each of its two 2-digit parts is square

**1682** is the number of monoids of order 7 with 7 idempotents

**1683** is a Delannoy number

**1684** is the number of multigraphs with 6 vertices and 9 edges

**1688** is a truncated tetrahedral number

**1689** is the smallest composite number all of whose proper divisors contain the digit 9

**1690** is the number of ordered sequences of coins totaling 27 cents

**1691** is the number of multigraphs with 5 vertices and 11 edges

**1692** has a square with the first 3 digits the same as the next 3 digits

**1694** has a cube whose digits occur with the same frequency

**1695** is a rhombic dodecahedral number

**1696** is the number of regions formed when all diagonals are drawn in a regular 16-gon

**1700** is the generalized Catalan number C(13,4)

**1701** is the Stirling number of the second kind S(8,4)

**1702** has a square that contains the same digits as 13^{6}

**1705** is the smallest quasi-Carmichael number in base 4

**1709** is the index of a Wagstaff prime

**1710** is the smallest non-palindrome where it and its reverse are divisible by 19

**1711** is a triangular number that is the product of two primes

**1712** is the number of regions the complex plane is cut into by drawing lines between all pairs of 16^{th} roots of unity

**1713** is the number of 14-iamonds with holes

**1714** is the number of graphs with 9 vertices and 7 cycles

**1715** = 1 × 7^{3} × 1 × 5

**1716** = _{13}C _{6}

**1722** is a Giuga number

**1725** is a structured deltoidal hexacontahedral number

**1727** and its reverse are both differences of positive cubes

**1728** = 12^{3}

**1729** is a taxicab number

**1730** is the sum of consecutive squares in 2 ways

**1731** is the sum of the squares of 3 consecutive primes

**1734** is the sum of its proper divisors that contain the digit 8

**1736** is the number of ways to place 2 non-attacking bishops on a 8×8 chessboard

**1737** is a value of n so that (n-1)^{2} + n^{2} + (n+1)^{2} is a palindrome

**1738** = 6952 / 4, and this equation uses each digit 1-9 exactly once

**1739** is a value of n for which n^{8}, n^{9}, n^{10}, and n^{11} have the same digit sum

**1740** has a base 5 representation that begins with its base 9 representation

**1741** is the smallest prime so that it and the next 5 primes are all equal to 1 (mod 6)

**1747** is a value of n for which n (n+2) is a palindrome

**1749** is the number of digits in the 4^{th} Cullen prime

**1751** is the 6^{th} central pentanomial coefficient

**1753** is the largest prime factor of 8! - 1

**1755** = 3333 in base 8

**1756** is the number of ways to stack 28 boxes in a line so that each box lies on the table or on a box next to 2 boxes

**1757** is the smallest multi-digit number n, that when interpreted in base 17, gives a multiple of n

**1759** is an Eisenstein-Mersenne prime (A066408)

**1763** is the product of twin primes

**1764** is the Stirling number of the first kind s(7,2)

**1769** is the 4-digit string that appears latest in the decimal expansion of e

**1770** is the number of conjugacy classes in the automorphism group of the 13 dimensional hypercube .

**1771** is a tetrahedral palindrome

**1775** is a member of the Fibonacci -type sequence starting with 1 and 7

**1779** is the smallest number whose 4^{th} power has 13 digits

**1780** is a structured truncated tetrahedral number

**1782** is the smallest number n that is 3 times the sum of all the 2-digit numbers that can be made using the digits of n

**1785** is a Kaprekar constant in base 2

**1786** has a cube that contains only digits 5 and larger.

**1787** is the number of different arrangements (up to rotation and reflection) of 12 non-attacking queens on a 12×12 chessboard

**1789** is the smallest number with the property that its first 4 multiples contain the digit 7

**1792** is a Friedman number

**1793** is a Pentanacci number

**1794** has a base 5 representation that begins with its base 9 representation

**1795** has a base 5 representation that begins with its base 9 representation

**1798** is a value of n for which φ (σ (n)) = φ (n)

**1799** is the sum of the cubes of 3 consecutive primes

**1800** is a pentagonal pyramidal number

**1801** is a Cuban prime

**1804** is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole on a side

**1805** has the property that if each digit is replaced by its square , the resulting number is a square

**1806** is a Schröder number

**1807** is a member of Sylvester's sequence

**1813** is the number of trees on 15 vertices with diameter 8

**1815** has a 4^{th} power in base 7 with no isolated digits

**1816** is the number of partitions of 44 into distinct parts

**1817** is the number of polyominoes with 8 or fewer squares

**1818** evenly divides the sum of its rotations

**1819** has a 7^{th} power that contains the same digits as 322^{9}

**1820** = _{16}C _{4}

**1822** has a cube that contains only even digits

**1823** has a square with the first 3 digits the same as the next 3 digits

**1824** has a cube that contains only even digits

**1825** is the smallest number whose square begins with three 3's

**1826** has the property that the sum of its prime factors is equal to the product of its digits

**1827** is a vampire number

**1828** is the 6^{th} meandric number and the 11^{th} open meandric number

**1830** is the number of ternary square-free words of length 19

**1831** is the smallest prime that is followed by 15 composite numbers .

**1834** is an octahedral number

**1835** is the number of Pyramorphix puzzle positions that require exactly 4 moves to solve

**1836** has a 4^{th} power whose product of digits is also a 4^{th} power

**1837** is a value of n for which 2n and 7n together use the digits 1-9 exactly once

**1840** are the first 4 digits of 1^{1} + 2^{2} + 3^{3} + ^{ . . .} + 1840^{1840}

**1842** is the number of rooted trees with 11 vertices (A000081)

**1843** has a square root whose decimal part starts with the digits 0-9 in some order

**1847** is the number of 2×2×2 Rubik's cube positions that require exactly 4 moves to solve

**1848** is the smallest value of n for which _{2n}C _{n} is divisible by n^{2}

**1849** is the smallest composite number all of whose proper divisors contain the digit 4

**1850** = (10^{3} + 10^{4} + 10^{5}) / (3 × 4 × 5)

**1851** is the number of inequivalent asymmetric Ferrers graphs with 28 points

**1854** is the number of derangements of 7 items

**1855** is the number of permutations of 7 items that fix 1 element

**1858** is the number of isomers of C_{14}H_{30}

**1860** is the number of ways to 12-color the faces of a tetrahedron

**1862** is the number of Chess positions that can be reached in only one way after 2 moves by white and 1 move by black

**1863** is the larger number in a Ruth-Aaron pair

**1865** = 12345 in base 6

**1866** is the number of inequivalent Ferrers graphs with 28 points

**1868** is the smallest number that can not be formed using the digit 1 at most 20 times, together with the symbols +, × and ^

**1869** is the closest integer to 11^{π }

**1870** is the product of two consecutive Fibonacci numbers

**1871** is a number n for which n, n+2, n+6, and n+8 are all prime

**1873** is a value of n for which one less than the product of the first n primes is prime

**1875** is the smallest order for which there are 21 groups

**1876** is the closest integer to 16^{e }

**1880** is a number whose sum of squares of the divisors is a square

**1883** is the number of conjugacy classes of the alternating group A_{28}

**1885** is a Zeisel number

**1889** is the smallest prime so that it and the next 4 primes are all equal to 5 (mod 6)

**1890** is the number of permutations of 10 items that fix 6 elements

**1891** is a triangular number that is the product of two primes

**1893** is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole in a corner

**1895** is a value of n for which n, 2n, 3n, 4n, 5n, and 6n all use the same number of digits in Roman numerals .

**1896** is the number of graphs with 9 vertices with clique number 2

**1897** is a Padovan number

**1898** is a value of n for which σ (n) = φ (n) + φ (n-1) + φ (n-2)

**1900** is the largest palindrome in Roman numerals

**1902** has a cube that contains only even digits

**1903** is the smallest number requiring an addition chain of length 15

**1905** is a Kaprekar constant in base 2

**1907** is a value of n for which n (n+2) is a palindrome

**1908** is the number of self-dual planar graphs with 22 edges

**1911** is a heptagonal pyramidal number

**1912** is a structured octagonal anti-diamond number

**1913** is prime and contains the same digits as the next prime

**1915** is the number of semigroups of order 5

**1916** is the number of ways to tile a 6×5 rectangle with integer -sided squares

**1917** is the number of possible configurations of pegs (up to symmetry) after 27 jumps in solitaire

**1919** is a member of the Fibonacci -type sequence starting with 2 and 7

**1920** is the smallest number that contains more different digits than its cube

**1921** has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers

**1923** is the smallest number whose cube contains 5 consecutive 1's

**1925** is a hexagonal pyramidal number

**1931** is the smallest number whose 7^{th} power has 23 digits

**1932** is 1/23 of the 23^{rd} Fibonacci number

**1933** is a prime factor of 111111111111111111111

**1934** is the smallest number so that it and the next 11 numbers all have an even number of prime factors

**1935** is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 17 stamps

**1936** is a Hexanacci number

**1937** is the number of digits of the 18^{th} perfect number (A061193)

**1941** is the maximum number of regions a circle can be cut into by joining 15 points on the circumference with straight lines

**1942** is the smallest number whose cube contains 5 consecutive 8's

**1944** is a member of the Fibonacci -like multiplication series starting with 2 and 3

**1945** is the number of triangles of any size contained in the triangle of side 19 on a triangular grid

**1947** is the number of planar partitions of 16

**1948** is the number of 4×4 sliding puzzle positions that require exactly 10 moves to solve starting with the hole in a corner

**1950** = (144 + 145 + . . . + 156) = (157 + 158 + . . . + 168)

**1952** + 2 is the sum of the proper divisors of 1952

**1953** is a Kaprekar constant in base 2

**1954** is the number of subsets of {1, 2, 3, ... 16} that do not contain solutions to x + y = z

**1956** is the number of ways to color the vertices of a triangle with 18 colors, up to rotation

**1957** is the number of permutations of some subset of 6 elements

**1958** is the number of partitions of 25

**1959** is a Lucas 7-step number

**1960** is the Stirling number of the first kind s(8,5)

**1961** is a strobogrammatic number

**1962** is the smallest value of n for which 2n and 9n together use the digits 1-9 exactly once

**1963** = 7852 / 4, and this equation uses each digit 1-9 exactly once

**1964** is the number of legal knight moves in Chess

**1966** has a cube that contains only digits 5 and larger.

**1969** is the only known counterexample to a conjecture about modular Ackermann functions

**1973** has a 4^{th} power that is 1/2 of the sum of three 4^{th} powers

**1976** is the maximum number of regions space can be divided into by 19 spheres

**1979** has a 6^{th} root whose decimal part starts with the digits 1-9 in some order

**1980** is the number of ways to fold a 2×4 rectangle of stamps

**1983** is a Perrin number

**1990** is a stella octangula number

**1991** are the first 4 digits of 6^{1991}

**1994** is the number of digits in the 5^{th} Cullen prime

**1995** is the number of graphs with 9 vertices with clique number 6

**1997** is a prime factor of 87654321

**1998** is the largest number that is the sum of its digits and the cube of its digits

**1999** is the smallest number whose digits add to 28