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 = 10³ (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 = 8¹ + 8⁰ + 8³ + 8³

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 2¹⁰⁵³ × 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 = 1² + 2³ + 3⁴ + 4⁵

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 = ₃₃C ₁ + ₃₃C ₁ + ₃₃C ₂ + ₃₃C 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 2¹¹⁴⁶ × 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 1⁷ + 2⁷ + 3⁷ + 1⁷ = 1231₈

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

1233 = 12² + 33²

1234 is the smallest 4-digit number with increasing digits

1236 is the number of conjugacy classes of the alternating group A₂₆

1238 is the number of rooted ternary trees with 11 vertices

1239 is a value of n for which n⁸, n⁹, n¹⁰, and n¹¹ 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 164⁷

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 = ₁₃C 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 1292¹²⁹²

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 8¹²⁹⁹

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 = 1304₆ + 1304₉

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

1306 = 1¹ + 3² + 0³ + 6⁴

1307 is a number n for which n²+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 K₁₉

1320 = ₁₂P 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 = ₂₁C 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 = ₁₅C 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 = 1² + 37² + 0²

1371 = 1² + 37² + 1²

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 + 3⁴ + 8 + 6⁴

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 n² and n³ 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 A₂₇

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 2¹⁵⁴²

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 1¹ + 2² + 3³ + ^{. . .} + 1577¹⁵⁷⁷

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 = 3153₈

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 = 1¹ + 6² + 7³ + 6⁴

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 13⁶

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 × 7³ × 1 × 5

1716 = ₁₃C ₆

1722 is a Giuga number

1725 is a structured deltoidal hexacontahedral number

1727 and its reverse are both differences of positive cubes

1728 = 12³

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 + n² + (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 n⁸, n⁹, n¹⁰, and n¹¹ 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 [large] Schröder number (A006318). It is also the 4^th primary pseudoperfect number (A054377).

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 322⁹

1820 = ₁₆C 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 1¹ + 2² + 3³ + ^{. . .} + 1840¹⁸⁴⁰

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 _2nC _n is divisible by n²

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

1850 = (10³ + 10⁴ + 10⁵) / (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 C₁₄H₃₀

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 A₂₈

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 6¹⁹⁹¹

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