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ΑΡΙΘΜΟΙ 1001 - 2000

1001 is the smallest palindromic product of 3 consecutive primes.

1002 is the number of partitions of 22.

1003 has a base 2 representation that ends with its base 3 representation.

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.

1017 is the smallest number whose square contains 7 different digits.

1018 is the number of isohedral 8-hexes.

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.

1028 only requires the digits 0-9 to be written in bases 2-18.

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.

1039 is the number of different resistances that can be formed by nine or fewer 1-ohm resistors in series or parallel.

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.

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

1049 is an Eisenstein-Mersenne prime.

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.

1061 is the smallest emirp which is a different emirp when viewed upside down.

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 e⁷.

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.

1102 is the number of connected graphs with 10 vertices and 36 edges.

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.

1115 is a number n for which φ(n) is a repdigit.

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 = ₃₃C₁ + ₃₃C₁ + ₃₃C₂ + ₃₃C₂.

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.

1150 is the number of 11-iamonds without bilateral symmetry.

1151 is the smallest number that can be written as the sum of consecutive primes in exactly 4 ways.

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.

1169 is the number of connected graphs with 8 vertices and 12 edges.

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.

1204 is the magic constant for a 7×7×7 magic cube.

1205 is the number of fullerenes with 58 carbon atoms.

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.

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.

1237 is the smallest prime that contains exactly 5 smaller primes as substrings.

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).

1258 is the number of commutative asymmetric semigroups of order 6.

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.

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 = ₁₃C₅.

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

1289 is a truncated octahedral number.

1290 is the number of connected graphs with 8 vertices and 16 edges.

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 = ₁₂P₃.

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 = ₂₁C₃.

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.

1338 is a number n for which φ(n) is a repdigit.

1340 has a square with a digit sum larger than its 5^th power.

1341 is a number n for which φ(n) is a repdigit.

1342 is the smallest number that is 15 away from a prime.

1343 is the smallest number that is 16 away from a prime.

1344 is the order of a perfect group.

1345 is the number of permutations of 8 elements that have 5^th power equal to the identity permutation.

1347 is the concatenation of the first 4 Lucas numbers.

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 e¹³⁵¹ 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.

1358 is a value of n for which n!!!! + 1 is prime.

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 = ₁₅C₄.

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.

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!.

1389 is the number of unit interval graphs with 9 vertices.

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.

1418 is the number of (not necessarily distinct) sets of Egyptian fractions that sum to 1 with smallest fraction 1/18.

1419 is a Zeisel number.

1420 + σ(1420) = 4444.

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.

1450 is the total number of labeled graphs on 0-5 vertices.

1451 is the 5^th central heptanomial coefficient.

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....

1492 is the number of lines passing through at least 2 points of an 9×9 grid of points.

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.

1507 is the number of partitions of 32 that do not contain 1 as a part.

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.

1529 is the number of (not necessarily distinct) sets of Egyptian fractions that sum to 1 with smallest fraction 1/22.

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 tetrahedral 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.

1546 is the number of 5×5 binary matrices with at most one 1 in each row and column.

1547 is a hexagonal pyramidal number.

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

1551 is the number of trees on 25 vertices with diameter 4.

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.

1590 is the denominator of the 52^nd Bernoulli number.

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.

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).

1625 is the number of circular permutations of a set with 8 elements with no element being mapped to its successor.

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.

1631 is the number of ordered subsets of {1,2,3,4,5} than contain the number 1.

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 with the property that the root-mean-square of its divisors is an integer.

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.

1697 is the smallest prime factor of 26! + 1.

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.

1706 = 5 × 6 × 7 × 8 + 5 + 6 + 7 + 8.

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 = ₁₃C₆.

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.

1733 is the smallest prime that contains exactly 6 smaller primes as substrings.

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.

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.

1778 is the largest number whose square has 5 digits.

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.

1784 is a number n for which φ(n) is a repdigit.

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.

1812 is the number of fullerenes with 60 carbon atoms.

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 = ₁₆C₄.

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.

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.

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.

2000 = 5555 in base 7.