BETA SAÚDE
1000 (number)
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| ||||
|---|---|---|---|---|
| Cardinal | one thousand | |||
| Ordinal | 1000th (one thousandth) | |||
| Factorization | 23 × 53 | |||
| Divisors | 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 | |||
| Greek numeral | ,Α´ | |||
| Roman numeral | M, m | |||
| Roman numeral (unicode) | M, m, ↀ | |||
| Unicode symbol | ↀ | |||
| Greek prefix | chilia | |||
| Latin prefix | milli | |||
| Binary | 11111010002 | |||
| Ternary | 11010013 | |||
| Senary | 43446 | |||
| Octal | 17508 | |||
| Duodecimal | 6B412 | |||
| Hexadecimal | 3E816 | |||
| Tamil | ௲ | |||
| Chinese | 千 | |||
| Punjabi | ੧੦੦੦ | |||
| Devanagari | १००० | |||
| Armenian | Ռ | |||
| Egyptian hieroglyph | 𓆼 | |||
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
A group of one thousand units is sometimes known, from Ancient Greek, as a chiliad.[1] A period of one thousand years may be known as a chiliad or, more often from Latin, as a millennium. The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand. It is the first 4-digit integer.
Notation
- The decimal representation for one thousand is
- 1000—a one followed by three zeros, in the general notation;
- 1 × 103—in engineering notation, which for this number coincides with:
- 1 × 103 exactly—in scientific normalized exponential notation;
- 1 E+3 exactly—in scientific E notation.
- The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024 or 210).
- In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
- Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30,000 or using "Y2K" to denote the Year 2000 computer problem.
- A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States, this is sometimes abbreviated with a "G" suffix.
In mathematics
Numbers in the range 1001–1999
1001 to 1099
1001
1004
1004 = 22 × 251. It is a heptanacci number.[3]
1009
1009 is the smallest four-digit prime, a Lucky prime, and Chen prime. It is palindromic in bases 11, 15, 19, 24 and 28: (83811, 47415, 2F219, 1I124, 18128).
1011
1011 = 3 × 337. It is a Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases). It is the largest natural number n such that 2n contains 101 and does not contain 11011. There are 1011 partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction.[4]
1013
1013 is a prime number, a Sophie Germain prime,[5] and a centered square number,[6]
1016
1016 = 23 × 127. It is stella octangula number and a member of the Mian–Chowla sequence.[7] There are 1016 surface points on a cube with edge-length 14.[8]
1019
1019 is a Sophie Germain prime,[5] a safe prime,[9] and a Chen prime.
1021
1021 is a Lucky prime and a twin prime with 1019.
1023
1024
1025
1025 = 52 × 41. It is a Jacobsthal-Lucas number and the hypotenuse of a primitive Pythagorean triangle. It is a Proth number because 1025 = 210 + 1. It is a member of the Moser–de Bruijn sequence because its base-4 representation (1000014) contains only digits 0 and 1, or equivalently, it's a sum of distinct powers of 4 (45 + 40).
1028
1028 = 22 × 257. It is sum of totient function for first 58 integers.
1029
There are 1029 primes <= 213.[10]
1031
1031 is a prime number, a Sophie Germain prime,[5] a super-prime, and a Chen prime. It is the exponent and number of ones for the fifth base-10 repunit prime.[11]
1033
1033 is a prime number and an emirp. It forms a twin prime pair with 1031.
1035
1035 = 32 × 5 × 23. It is a hexagonal number[12] and the 45th triangular number.[13]
1039
1039 is a Chen prime and a Lucky prime. There are 1039 partitions of 30 that do not contain 1 as a part.[14]
1040
1040 = 24 × 5 × 13. There are 1040 pieces that could be seen in a 6 × 6 × 6 × 6 Rubik's Tesseract.
1046
1046 = 2 × 523. It is a coefficient of f(q), the 3rd order mock theta function.[15]
1049
1049 is a prime number, a Sophie Germain prime,[5] a highly cototient number,[16] and a Chen prime.
1051
1051 is a prime number, a centered pentagonal number,[17] and a centered decagonal number.
1056
1056 = 25 × 3 × 11. It is a pronic number.[18]
1060
1060 = 22 × 5 × 53. It is the sum of the first twenty-five primes from 2 through 97 (the number of primes less than 100)[19] and the sixth sum of 10 consecutive primes, starting with 23 through 131.[20]
1061
1061 is a prime number, an emirp, and a twin prime with 1063. There are 1061 prime numbers between 1000 and 10000 (or, number of four-digit primes in decimal representation).[21]
1063
1063 is a prime number, a super-prime, a twin prime with 1061, and the sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167)
1069
1076
1076 = 22 × 269. There are 1076 strict trees weight 11.[23]
1078
1078 = 2 × 72 × 11. It is an Euler transform of negative integers.[24]
1080
1080 = 23 × 33 × 5. It is a pentagonal number[25] and a largely composite number.[26]
1081
1081 = 23 × 47. It is the 46th triangular number[13] and a member of Padovan sequence.[27]
1086
1086 = 2 × 3 × 181. It is a Smith number[28] and the sum of totient function for the first 59 integers.
1087
1087 is a prime number, a super-prime, a cousin prime, and a lucky prime.[29]
1089
1091
1091 is a prime number, a cousin prime, and a twin prime with 1093.
1093
1093 is a twin prime with 1091. Together with 1091 and 1097, it forms a prime triplet. It is a happy prime and a star[30] prime. It is also the smallest Wieferich prime. 1093 is a repunit prime in base 3 because:
1097
1097 is a prime number, an emirp,[22] and a Chen prime.
1100 to 1199
1102
1102 = 2 × 19 × 29. It is the sum of the totient function for the first 60 integers.
1103
1103 is a prime number, a Sophie Germain prime,[5] and a balanced prime.[31]
1104
1104 = 24 × 3 × 23. It is a Keith number[32]
1105
1109
1109 is a Chen prime.
1113
1113 = 3 × 7 × 53. There are 1113 strict partions of 40.[33]
1117
1117 is a Chen prime. There are 1117 diagonally symmetric polyominoes with 16 cells.[34]
1118
1118 = 2 × 13 × 43. There are 1118 unimodular 2 × 2 matrices having all terms in {0,1,...,21}.[35]
1119
1119 = 3 × 373. There are 1119 bipartite graphs with 9 nodes.[36]
1122
1122 = 2 × 3 × 11 × 17. It is a pronic number.[18]
1123
1123 is a balanced prime.[31]
1126
1126 = 2 × 563. There are 1126 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}.[37]
1127
1127 = 72 × 23. It is the maximum number of pieces that can be obtained by cutting an annulus with 46 cuts.[38]
1128
1128 = 23 × 3 × 47. It is the 47th triangular number[13] and the 24th hexagonal number.[12] 1128 is the dimensional representation of the largest vertex operator algebra with central charge of 24, D24.[39]
1151 is the first prime number following a prime gap of 22.[40] It is also a Chen prime.
1152
1152 = 27 × 32. It is a highly totient number,[41] a 3-smooth number, and an Achilles number.
1153
1153 is a super-prime and a Proth prime.[42]
1159
1159 = 19 × 61. It is a centered octahedral number[43] and a member of the Mian–Chowla sequence.[7]
1160
1160 = 23 × 5 × 29. It is an octagonal number.[44]
1161
1161 = 33 × 43. It is the sum of the first twenty-six primes.
1162
1162 = 2 × 7 × 83. It is the sum of the totient function for the first 61 integers and a pentagonal number.[25]
1163
1163 is a Chen prime.
1164
1164 = 22 × 3 × 97. There are 1164 chains of multisets that partition a normal multiset of weight 8, where a multiset is normal if it spans an initial interval of positive integers[45]
1169
1169 = 7 × 167. It is a highly cototient number[16]
1171
1171 is a super-prime.[citation needed]
1173
1173 = 3 × 17 × 23. There are 1173 simple triangulations on a plane with 9 nodes.[46]
1174
1174 = 2 × 587. There are 1174 widely totally strongly normal compositions of 16. (sequence A332337 in the OEIS).
1175
1175 = 52 × 47. It is the maximum number of pieces that can be obtained by cutting an annulus with 47 cuts.[38]
1176
1176 = 23 × 3 × 72. It is the 48th triangular number.[13]
1178
1178 = 2 × 19 × 31. There are 1178 surface points on a cube with edge-length 15.[8]
1179
1179 = 32 × 131. There are 1179 different permanents of binary 7 by 7 matrices.[47]
1182
1182 = 2 × 3 × 197. There are 1182 necklaces possible with 14 beads of 2 colors (that cannot be turned over).[48]
1184
1184 = 25 × 37. It is an amicable number with 1210.[49]
1186
1186 = 2 × 593. There are 1186 diagonally symmetric polyominoes with 15 cells.[34]
1187
1187 is a safe prime,[9] a Stern prime,[50] a balanced prime,[31] and a Chen prime.
1190
1190 = 2 × 5 × 7 × 17. It is a pronic number.[18] Building a 28-tier house of cards requires 1190 cards.[51]
1191
1191 = 3 × 397 = 352 - 35 + 1 = H35, the 35th Hogben number.[52]
1192
1192 = 23 × 149. It is the sum of the totient function for the first 62 integers.
1193
1193 is a Chen prime.
1198
1198 = 2 × 599. It is a centered heptagonal number.[53]
1200 to 1299
1200
1200 = 24 × 3 × 52. There are 1200 households in the Nielsen ratings sample.[54]
1200 is known as the long thousand or ten "long hundreds" of 120 each. It is the traditional reckoning of large numbers in Germanic languages.
1201
1201 is a super-prime, a centered square number,[6] and a centered decagonal number.
1202
1202 = 2 × 601. There are a maximum of 1202 regions when the plane is divided by 25 ellipses.[55]
1203
1203 = 3 × 401. It is the smallest number greater than 1000 in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane.[56]
1204
1204 = 22 × 7 × 43. It is the magic constant for a 7 × 7 × 7 magic cube.[57]
1205
1205 = 5 × 241. There are 1205 partitions of 28 such that the number of odd parts is a part[58]
1207
1207 = 17 × 71. It is a composite de Polignac number.[59]
1208
1208 = 23 × 151. There are 1208 strict chains of divisors starting with the superprimorial A006939(3).[60]
1210
1210 = 2 × 5 × 112. It is an amicable number with 1184[61] and a Self-descriptive number.
1211
1211 = 7 × 173. It is a composite de Polignac number[59]
1212
1212 = 22 × 3 × 101 = , where is the number of partions of .[62]
1213
1213 is a prime number and an emirp.
1214
1214 = 2 × 607. It is a spy number and the sum of the first 39 composite numbers.[63]
1215
1215 = 35 × 5. There are 1215 edges in the hexagonal triangle T(27)[64]
1216
1216 = 26 × 19. It is a nonagonal number[65]
1217
1217 is a super-prime and a Proth prime.[42]
1219
1219 = 23 × 53. It is a centered triangular number[66] and a zero of Mertens function.
1220
1220 = 22 × 5 × 61. It is a zero of Mertens function. There are 1220 binary vectors of length 16 containing no singletons.[67]
1222
1222 = 2 × 13 × 47. It is a hexagonal pyramidal number.
1223
1223 is the 200th prime number.[31] It is also a Sophie Germain prime[5] and a balanced prime.
1224
1224 = 23 × 32 × 17. There are 1224 edges in the join of two cycle graphs, both of order 34.[68]
1225
1225 = 52 × 72 = 352. It is the smallest number greater than 1 to be a triangular number,[13] a square number and a hexagonal number.[12][69] It is the second square triangular number greater than 1.[70] It is the 49th triangular number, the 35th square number, the 25th hexagonal number, a centered octagonal number,[71] a 29-gonal number,[72] a 60-gonal number,[73] and a 124-gonal number. It is the sum of 5 consecutive odd cubes:
1225 = 13 + 33 + 53 + 73 + 93.
1226
1226 = 2 × 613. There are 1226 rooted identity trees with 15 nodes.[74]
1228
1228 = 22 × 307. It is the sum of the totient function for the first 63 integers.
1229
1229 is a Sophie Germain prime[5] and an emirp. There are 1229 primes less than 10,000.
1230
1230 = 2 × 3 × 5 × 41 = T(9, 6), the Mahonian number.[75]
1231
1231 is a prime number and an emirp.
1232
1232 = 24 × 7 × 11. There are 1232 labeled ordered set of partitions of a 7-set into odd parts.[76]
1234
It has two distinct prime factors, 2 and 617,[77] making it a squarefree semiprime.[78] It is the number of independent vertex sets in a 4×4 square grid, or equivalently, the number of distinct 4×4 binary matrices in which no two adjacent elements are both equal to 1.[79]
1240
1240 = 23 × 5 × 31. It is a square pyramidal number.[80]
1241
1241 = 17 × 73. It is a centered cube number[81] and a spy number.
1243
1243 = 11 × 113. It is a composite de Polignac number.[59]
1244
1244 = 22 × 311. There are 1244 complete partitions of 25.[82]
1245
1245 = 3 × 5 × 83. There are 1245 labeled spanning intersecting set-systems on 5 vertices.[83]
1247
1247 = 29 × 43. It is a pentagonal number.[25]
1249
1249 is a prime number, an emirp, and a trimorphic number.[84]
1257
1257 = 3 × 419. There are 1257 lattice points inside a circle of radius 20.[85]
1259
1259 is a prime number and a highly cototient number.[16]
1260
1260 = 22 × 32 × 5 × 7. It is a pronic number,[18] the smallest vampire number,[86] the 16th highly composite number,[87] and the sum of the totient function for the first 64 integers. There are 1260 strict partions of 41.[33]
1261
1261 = 13 × 97. It is a star number[30] and a zero of Mertens function.
1264
1264 = 24 × 79. It is the sum of the first 27 primes.
1265
1265 = 5 × 11 × 23. There are 1265 rooted trees with 43 vertices in which vertices at the same level have the same degree.[88]
1266
1266 = 2 × 3 × 211. It is a centered pentagonal number[17] and a zero of Mertens function.
1269
1269 = 33 × 47. Completing 11 revolutions in the Spiral of Theodorus requires 1269 triangles. [89]
1275
1275 = 3 × 52 × 17. It is the 50th triangular number.[13]
1276
1276 = 22 × 11 × 29. There are 1276 irredundant sets in the 25-cocktail party graph.[90]
1277
1277 is a prime number. It is the start of a prime constellation of length 9 (a "prime nonuple").
1278
1278 = 2 × 32 × 71. There are 1278 Narayana's cows and calves after 20 years.[91]
1279
1279 is a prime number and a Mersenne prime exponent.
1280
1280 = 28 × 5. There are 1280 parts in all compositions of 9.[92]
1281
1281 = 3 × 7 × 61. It is an octagonal number.[44]
1283
1283 is a safe prime.[9]
1284
1284 = 22 × 3 × 107 = 641 + 643, the sum of a twin prime pair.[93]
1285
1285 = 5 × 257. There are 1285 free nonominoes.
1286
1286 = 2 × 643. There are 1286 inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree.[94]
1288
1288 = 23 × 7 × 23. It is a heptagonal number.[95]
1289
1289 is Sophie Germain prime[5] and a twin prime with 1291. 1289 is a deficient number because the sum of all its positive divisors (except itself) totals less than 1289. 1289 is an evil number because it has an even number of 1's contained in its binary expansion.
1291
1291 is a twin prime with 1289.
1296
1296 = 24 × 34 = 64 = 362. It is the sum of the cubes of the first eight positive integers:
13 + 23 + 33 + 33 + 43 + 53 + 63 + 73 + 83 = 1296.
There are 1296 rectangles on a normal 8 × 8 chessboard. There are 1296 combinations of 2 alphanumeric characters.
1297
1297 is a super-prime, a pinwheel number,[96] and a zero of Mertens function.
1300 to 1399
1300
1300 = 22 × 52 × 13. It is a zero of Mertens function and the smallest even odd-factor hyperperfect number. It is the sum of the first 4 fifth powers:
1300 = 15 + 25 + 35 + 45.
1301
1301 is a prime number and a centered square number.[6] There are 1301 trees with 13 unlabeled nodes.[97]
1306
1306 = 2 × 653. It is a centered triangular number.[66]
1307
1307 is a safe prime.[9]
1308
1308 = 22 × 3 × 109. It is the sum of the totient function for the first 65 integers.
1312
1312 = 25 × 41. It is a member of the Mian-Chowla sequence.[7]
1319
1319 is a safe prime.[9]
1325
1325 = 52 × 53. It is a Markov number[98] and a centered tetrahedral number.[99]
1326
1326 = 2 × 3 × 13 × 17. It is the 51st triangular number[13] and a hexagonal number.[12]
1327
1327 is the smallest prime number preceding a prime gap of 34.
1328
1328 = 24 × 83. It is the sum of the totient function for the first 66 integers.
1330
1330 = 2 × 5 × 7 × 19. It is a tetrahedral number.[100] It forms a Ruth–Aaron pair with 1331 under second definition.
1331
1331 = 113. It is a centered heptagonal number.[53] It forms a Ruth–Aaron pair with 1330 under second definition.
1335
1335 = 3 × 5 × 89. It is a pentagonal number.[25]
1342
1342 = 2 × 11 × 61 = .[101]
1346
1346 = 2 × 673. There are 1346 locally disjointed rooted trees with 10 nodes.[102]
1350
1350 = 2 × 33 × 52. It is a nonagonal number.[65]
1361
1361 is first prime number following a prime gap of 34[40] and the 3rd Mills' prime. It is a centered decagonal number
1364
1364 = 22 × 11 × 31. It is a Lucas number.[103]
1365
1365 = 3 × 5 × 7 × 13. It is a pentatope number.[104]
1367
1367 is a safe prime[9] and a balanced prime. It is the sum of three, nine, and eleven consecutive primes: (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),[31]
1371
1371 = 3 × 457. It is the sum of the first 28 primes.
1377
1377 = 34 × 17. It is the maximal number of pieces that can be obtained by cutting an annulus with 51 cuts[38]
1378
1378 = 2 × 13 × 53. It is the 52nd triangular number[13]
1379
1379 = 7 × 197. It is the magic constant of n × n normal magic square and n-queens problem for n = 14.
1380
1380 = 22 × 3 × 5 × 23. There are 1380 8-step mappings with 4 inputs.[105]
1381
1381 is a prime number and a centered pentagonal number.[17]
1384
1384 = 23 × 173 = [101]
1385
1385 = 5 × 277. It is an up/down number.[106]
1387
1387 = 19 × 73. It is the 5th Fermat pseudoprime of base 2,[107] the 22nd centered hexagonal number, the 19th decagonal number,[108] and the second Super-Poulet number.[109]
1388
1388 = 22 × 347. Because 1388 = 4 × 192 - 3 × 19 + 1, is on the x-axis of Ulams spiral.[110]
1394
1394 = 2 × 17 × 41. It is the sum of the totient function for the first 67 integers.
1395
1395 = 32 × 5 × 19. It is a vampire number[86] and a member of the Mian–Chowla sequence[7]
1396
1396 = 22 × 349. It is a centered triangular number.[66]
1399
1399 is a prime number and an emirp.[111]
1400 to 1499
1403
1403 = 23 × 61. It is the smallest number x such that M(x) = 11, where M() is Mertens function[112]
1404
1404 = 22 × 32 × 13. It is a heptagonal number.[95]
1405
1405 = 5 × 281 = 262 + 272 = 72 + 82 + ... + 162. It is a centered square number[6]
1406
1406 = 2 × 19 × 37. It is a semi-meandric number.[113]
1409
1409 is a super-prime, a Sophie Germain prime,[5] and a Proth prime.[42]
1410
1410 = 2 × 3 × 5 × 47. It is the denominator of the 46th Bernoulli number[114]
1418
1418 = 2 × 709. It is the smallest number x such that M(x) = 13, where M() is Mertens function[112]
1425
1425 = 3 × 52 × 19. It is a self-descriptive number in base 5.
1426
1426 = 2 × 23 × 31. It is a pentagonal number[25] and the sum of the totient function for the first 68 integers. There are 1426 strict partions of 42.[33]
1427
1427 is a twin prime with 1429.[115]
1428
1428 = 22 × 3 × 7 × 17. There are 1428 complete ternary trees with 6 internal nodes or, equivalently, 18 edges.[116]
1429
1429 is a twin prime with 1427.[115]
1430
1430 = 2 × 5 × 11 × 13. It is a Catalan number.[117]
1431
1431 = 33 × 53. It is the 53rd triangular number[13] and a hexagonal number.[12]
1432
1432 = 23 × 179. It is a member of the Padovan sequence.[27]
1433
1433 is a super-prime.[118]
1435
1435 = 5 × 7 × 41. It is a vampire number.[86]
1436
1436 = 22 × 359. It is the discriminant of a totally real cubic field.[119]
1439
1440
1440 = 25 × 32 × 5. It is a highly totient number.[41]
1441
1441 = 11 × 131. It is a star number.[30]
1447
1447 is a super-prime number and a happy number.
1451
1451 is a Sophie Germain prime.[5]
1452
1452 = 22 × 3 × 112. It is the first Zagreb index of the complete graph K12.
1453
1453 is a Sexy prime with 1459.
1458
1458 = 2 × 36. It is the maximum determinant of an 11 by 11 matrix of zeroes and ones[120] and a 3-smooth number.
1458 is one of three numbers which, when its base 10 digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
1459
1459 is a Sexy prime with 1453 and a Pierpont prime. It is the sum of nine consecutive primes:
1459 = 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181.
1462
1462 = 2 × 17 × 43. Because 1462 = (35 - 1) × (35 + 8), it is the first Zagreb index of the wheel graph with 35 vertices[122]
1467
1467 = 32 × 163. There are 1467 partitions of 39 with zero crank.[123]
1469
1469 = 13 × 113. It is an octahedral number[124] and a highly cototient number.[16]
1470
1470 = 2 × 3 × 5 × 72. It is the sum of the totient function for the first 69 integers.
1476
1476 is the number of diamonds necessary to build a full, maximum-power (Level 4) pyramid for a Minecraft Beacon entirely out of diamond blocks.
1471
1471 is a super-prime number and a centered heptagonal number.[53]
1480
1480 = 23 × 5 × 37. It is the sum of the first 29 primes.
1481
1481 is a Sophie Germain prime.[5]
1485
1485 = 33 × 5 × 11. It is the 54th triangular number.[13]
1486
1486 = 2 × 743. There are 1486 strict solid partitions of 19.[125]
1487
1487 is a safe prime.[9]
1489
1489 is a prime number and a centered triangular number.[66]
1490
1490 = 2 × 5 × 149. It is a tetranacci number.[126]
1491
1491 = 3 × 7 × 71. It is a nonogonal number.[65]
1492
1492 = 22 × 373. It is the discriminant of a totally real cubic field.[119]
1493
1493 is a Stern prime.[50]
1494
1494 = 2 × 32 × 83. It is the sum of the totient function for the first 70 integers.
1496
1496 = 23 × 11 × 17. It is a square pyramidal number.[80]
1499
1499 is a Sophie Germain prime[5] and a super-prime.
1500 to 1599
1500
1500 = 22 × 3 × 53. It is the hypotenuse of three different Pythagorean triangles.[127]
1501
1501 = 19 × 79. It is a centered pentagonal number.[17]
1503
1503 = 32 × 167. Completing 12 revolutions of the Spiral of Theodorus requires 1503 triangles.[89]
1510
1510 = 2 × 5 × 151. 1510 is an untouchable number.
1511
1513
1513 = 17 × 89. It is a centered square number.[6]
1520
1520 = 24 × 5 × 19. It is a pentagonal number.[25] It forms a Ruth–Aaron pair with 1521 under the second definition.
1521
1521 = 32 × 132 = 392. It is a centered octagonal number.[71] It forms a Ruth–Aaron pair with 1520 under the second definition.
1523
1523 is a super-prime, a safe prime,[9] and a member of the Mian–Chowla sequence.[7]
1525
1525 = 52 × 61. It is a heptagonal number.[95]
1526
1526 = 2 × 7 × 109. There are 1526 conjugacy classes in the alternating group A27.[128]
1529
1529 = 11 × 139. It is a composite de Polignac number.[59]
1530
1530 = 2 × 32 × 5 × 17. It is a vampire number.[86]
1531
1531 is a prime number and a centered decagonal number.
1532
1532 = 22 × 383. There are 1532 series-parallel networks with 9 unlabeled edges,[129]
1535
1535 = 5 × 307. It is a Thabit number.
1537
1537 = 29 × 53. It is a Keith number.[32]
1539
1539 = 34 × 19. A maximum of 1539 pieces can be obtained by cutting an annulus with 54 cuts.[38]
1540
1540 = 22 × 5 × 7 × 11. It is the 55th triangular number,[13] a hexagonal number,[12] a decagonal number,[108] and a tetrahedral number.[100]
1541
1541 = 23 × 67. It is an octagonal number.[44]
1549
1549 is a de Polignac prime.[130]
1557
1557 = 32 × 173. There are 1557 graphs with 8 nodes and 13 edges.[131]
1559
1559 is a Sophie Germain prime.[5]
1561
1561 = 7 × 223. It is a centered octahedral number.[43]
1564
1564 = 22 × 17 × 23. It is the sum of the totient function for the first 71 integers.
1572
1572 = 22 × 3 × 131. It is a member of the Mian–Chowla sequence.[7]
1573
1573 = 112 × 13. It is the discriminant of a totally real cubic field.[119]
1583
1583 is a Sophie Germain prime.
1585
1585 = 5 × 307. It is a centered triangular number.[66]
1588
1588 = 22 × 397. It is the sum of the totient function for the first 72 integers.
1589
1589 = 7 × 227. It is a composite de Polignac number.[59]
1593
1593 = 33 × 59. It is the sum of the first 30 primes.
1594
1594 = 2 × 797. It is the minimal cost of a maximum height Huffman tree of size 17.[132]
1596
1596 = 22 × 3 × 7 × 19. It is the 56th triangular number.[13]
1597
1597 is a super-prime, a Fibonacci prime,[133] a Markov prime,[98] and an emirp.
1600 to 1699
1601
1601 is a Sophie Germain prime and a Proth prime.[42]
1607, 1609, and 1613
1607, 1609, and 1613 form a prime triple.
1617
1617 = 3 × 72 × 11. It is a pentagonal number.[25]
1618
1618 = 2 × 809. It is a centered heptagonal number.[53]
1619
1619 is a safe prime.[9]
1621
1621 is a super-prime.
1624
1624 = 23 × 7 × 29. There are 1624 squares in the Aztec diamond of order 28.[134]
1625
1625 = 53 × 13. It is a centered square number.[6]
1626
1626 = 2 × 3 × 271. It is a centered pentagonal number.[17]
1633
1633 = 23 × 71. It is a star number.[30]
1634
1634 = 2 × 19 × 43. It is the smallest four-digit Narcissistic number in base 10.
1637
1637 is a prime island: it is the smallest prime whose adjacent primes are exactly 30 apart.[135]
1638
1638 = 2 × 32 × 7 × 13. It is a harmonic divisor number.[136]
1639
1639 = 11 × 149. It is a nonagonal number.[65]
1646
1646 = 2 × 823. There are 1646 graphs with 8 nodes and 14 edges.[131]
1649
1649 = 17 × 97. It is a highly cototient number[16] and a Leyland number[137] using 4 and 5: 1649 = 45 + 54.
1651
1651 = 13 × 127. It is a heptagonal number.[95]
1653
1653 = 3 × 19 × 29. It is the 57th triangular number[13] and a hexagonal number.[12]
1657
1657 is a cuban prime.[138]
1660
1660 = 22 × 5 × 83. It is the sum of the totient function for the first 73 integers.
1665
1665 = 32 × 5 × 37. It is a centered tetrahedral number.[99]
1669
1669 is a super-prime. It is the smallest prime with a gap of exactly 24 to the next prime.[139]
1679
1679 = 23 × 73. It is a highly cototient number.[16]
1680
1680 = 24 × 3 × 5 × 7. It is the 17th highly composite number.[87]
1681
1681 = 412 = 402 + 40 + 41. It is the smallest number yielded by the formula n2 + n + 41, where n is a natural number, that is not a prime. It is also a centered octagonal number.[71]
1682 and 1683
1682 and 1683 form a Ruth–Aaron pair under the first definition.
1684
1684 = 22 × 421. It is a centered triangular number.[66]
1691
1691 = 19 × 89. It is a strobogrammatic number.[140]
1695
1695 = 3 × 5 × 113. It is the magic constant of n × n normal magic square and the n-queens problem for n = 15.
1696
1696 = 25 × 53. It is the sum of the totient function for the first 74 integers.
1700 to 1799
1705
1705 = 5 × 11 × 13. It is a tribonacci number.[141]
1710
1710 = 2 × 32 × 5 × 19. A maximum of 1710 pieces can be obtained by cutting an annulus 57 times.[38]
1711
1711 = 29 × 59. It is the 58th triangular number[13] and a centered decagonal number.
1717
1717 = 17 × 101. It is a pentagonal number.[25]
1719
1719 = 32 × 131. it is a composite de Polignac number.[59]
1720
1720 = 23 × 5 × 43. It is the sum of the first 31 primes.
1721
1721 is a twin prime with 1723.[142]
1722
1722 = 2 × 3 × 7 × 41. It is a Giuga number[143] and a pronic number.[18]
1723
1723 is a twin prime with 1721. It is also a super-prime.
1728
1729
1733
1733 is a Sophie Germain prime. It is palindromic in bases 3, 18, and 19.
1736
1736 = 23 × 7 × 31. It is the sum of the totient function for the first 75 integers.
1740
1740 = 22 × 3 × 5 × 29. There are 1740 squares in the Aztec diamond of order 29.[134]
1741
1741 is a super-prime and a centered square number.[6]
1747
1747 is a balanced prime.[31]
1750
1750 = 2 × 53 × 7. It is the hypotenuse of three different Pythagorean triangles with integer side lengths.[127]
1753
1753 is a balanced prime.[31]
1756
1756 = 22 × 439. It is a centered pentagonal number.[17]
1757
1757 = 7 × 251. Completing 13 revolutions around the Spiral of Theodorus requires 1757 triangles. [89]
1759
1759 is a de Polignac prime.[130]
1765
1765 = 5 × 353. There are 1765 planar partitions of 15.[144]
1769
1769 = 29 × 61. A maximum of 1769 pieces can be obtained by cutting an annulus with 58 times.[38]
1770
1770 = 2 × 3 × 59. It is the 59th triangular number[13] and a hexagonal number.[12]
1771
1771 = 7 × 11 × 23. It is a tetrahedral number.[100]
1772
1772 = 22 × 443. It is a centered heptagonal number[53] and the sum of the totient function for the first 76 integers.
1776
1776 = 24 × 3 × 37. It is the 24th square star number.[145] A total of 1776 pieces could be seen in a 7 × 7 × 7 × 7 Rubik's Tesseract.
1782
1782 = 2 × 34 × 11. It is a heptagonal number.[95]
1783
1783 is a de Polignac prime.[130]
1785
1785 = 3 × 5 × 7 × 17. It is a square pyramidal number.[80]
1786
1786 = 2 × 19 × 47. It is a centered triangular number.[66]
1787
1787 is a super-prime. It is the sum of eleven consecutive primes: 1787 = 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191.
1792
1792 = 28 × 7. It is a Granville number.
1794
1794 = 2 × 3 × 13 × 23. It is a nonagonal number.[65]
1800 to 1899
1801
1801 is a cuban prime. It is the sum of five consecutive primes (349 + 353 + 359 + 367 + 373) and nine consecutive primes 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227).[138]
1806
1806 = 2 × 3 × 301. It is a pronic number,[18] a primary pseudoperfect number,[146] and a Schröder number.[147] It is the only number n such that the denominator of the nth Bernoulli number is n.[148]
1807
1807 = 13 × 139. It is the fifth term of Sylvester's sequence.[149]
1811
1811 is a Sophie Germain prime.
1820
1820 = 22 × 5 × 7 × 13. It is a pentagonal number[25] and a pentatope number.[104]
1821
1821 = 3 × 607. It is a member of the Mian–Chowla sequence.[7]
1823
1823 is a super-prime and a safe prime.[9]
1825
1825 = 52 × 73. It is an octagonal number.[44]
1827
1827 = 32 × 7 × 29. It is a vampire number.[86]
1828
1828 = 22 × 457. It is a meandric number as well as an open meandric number.
1829
1829 = 31 × 59. composite de Polignac number.[59]
1830
1830 = 2 × 3 × 5 × 61. It is the 60th triangular number.[13]
1831
1831 is the smallest prime number with a gap of exactly 16 to the next prime, 1847.[150]
1834
1834 = 2 × 7 × 131. It is an octahedral number.[124]
1837
1837 = 11 × 167. It is a star number.[30]
1841
1841 = 7 × 263. It is the solution to the postage stamp problem with 3 denominations and 29 stamps.[151]
1847
1847 is a super-prime.
1859
1859 = 11 × 132. It is a composite de Polignac number.[59]
1861
1861 is a prime number and a centered square number.[6]
1862 and 1863
1862 and 1863 form a Ruth–Aaron pair under the second definition.
1867
1867 is a prime de Polignac number.[130]
1870
1870 = 2 × 5 × 11 × 17. It is a decagonal number.[108]
1871, 1873, 1877, and 1879
1871, 1873, 1877, and 1879 form a prime quadruple.[152]
There are 1873 Narayana's cows and calves after 21 years.[91]
1880
1880 = 23 × 5 × 47. It is the 10th element of the self convolution of Lucas numbers.[153]
1882
1882 = 2 × 941. There are 1882 linearly separable Boolean functions in 4 variables.[154]
1889
1889 is a Sophie Germain prime and a highly cototient number.[16]
1891
1891 = 31 × 61. It is the 61st triangular number,[13] a centered triangular number[66] a hexagonal number,[12] a centered pentagonal number,[17] and the sum of 5 consecutive primes: 1891 = 367 + 373 + 379 + 383 + 389.
1892
1892 = 22 × 11 × 43. It is a pronic number.[18]
1896
1896 = 23 × 3 × 79. It is a member of the Mian-Chowla sequence.[7]
1897
1897 = 7 × 271. It is a member of the Padovan sequence.[27]
1900 to 1999
- 1901 = Sophie Germain prime, centered decagonal number
- 1902 = number of symmetric plane partitions of 27[155]
- 1903 = generalized Catalan number[156]
- 1905 = Fermat pseudoprime[157]
- 1907 = safe prime,[9] balanced prime[31]
- 1909 = hyperperfect number[158]
- 1913 = super-prime
- 1918 = heptagonal number[95]
- 1926 = pentagonal number[25]
- 1931 = Sophie Germain prime
- 1933 = centered heptagonal number,[53]
- 1951 = cuban prime[138]
- 1953 = 62nd triangular number[13]
- 1956 = nonagonal number[65]
- 1964 = number of linear forests of planted planar trees with 8 nodes[159]
- 1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[160]
- 1973 = Sophie Germain prime, Leonardo prime
- 1976 = octagonal number[44]
- 1980 = pronic number,[18] highly abundant number with a greater sum of proper divisors than all smaller numbers[161]
- 1984 = 11111000000 in binary, nonunitary perfect number,[162]
- 1985 = centered square number[6]
- 1987 = 300th prime number
- 1990 = Stella octangula number
- 1991 = 11 × 181, the 46th Gullwing number,[163]
- 1999 = centered triangular number,[66] number of regular forms in a myriagram.
Prime numbers
There are 135 prime numbers between 1000 and 2000:[164][165]
- 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999
Notes
References
- ↑ "chiliad". Merriam-Webster.
{{cite web}}: CS1 maint: url-status (link) - ↑ Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers: a(n) equal to n*(499*n - 498))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A122189 (Heptanacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers <= n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 0"}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A005897 (6*n^2 + 2 for n > 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 10 11 12 Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes p: (p-1)/2 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000025 (Coefficients of the 3rd-order mock theta function f(q))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers: records for a(n) in A063741)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A006567 (Emirps (primes whose reversal is a different prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A273873 (Number of strict trees of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 10 Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts"}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A000096 (n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Van Ekeren, Jethro; Lam, Ching Hung; Möller, Sven; Shimakura, Hiroki (2021). "Schellekens' list and the very strange formula". Advances in Mathematics. 380 107567. Amsterdam: Elsevier. arXiv:2005.12248. doi:10.1016/j.aim.2021.107567. MR 4200469. S2CID 218870375. Zbl 1492.17027.
- 1 2 "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 July 2016.
- 1 2 "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 3 4 "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
- 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A055887 (Number of ordered partitions of partitions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "A000256 - OEIS". oeis.org.
- ↑ "1179 (number)". The encyclopedia of numbers.
- ↑ "A000031 - OEIS". oeis.org.
- ↑ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
- 1 2 "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers: n*(3*n + 1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
- ↑ Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "A265070 - OEIS". oeis.org.
- ↑ "1204 (number)". The encyclopedia of numbers.
- ↑ Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 7 8 Sloane, N. J. A. (ed.). "Sequence A098237 (Composite de Polignac numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A337070 (Number of strict chains of divisors starting with the superprimorial A006939(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Higgins, ibid.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000070 (Sum_{0..n} A000041(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ "A046177 - OEIS". oeis.org. Retrieved 18 December 2024.
- 1 2 3 "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A303815 (Generalized 29-gonal (or icosienneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A249911 (60-gonal (hexacontagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "A004111 - OEIS". oeis.org.
- ↑ Sloane, N. J. A. (ed.). "Sequence A008302 (Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product{0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "A006154 - OEIS". oeis.org.
- ↑ Vanovschi, Vitalii. "Properties of the number 1234". www.numberempire.com. Retrieved 9 August 2026.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006506". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ oeis.org/A305843
- ↑ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A003238 (Number of rooted trees with n vertices in which vertices at the same level have the same degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 Sloane, N. J. A. (ed.). "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A084849 (1 + n + 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001792 ((n+2)*2^(n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A216492 (Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A005894 (Centered tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A024916 (Sum_1^n sigma(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "A316473 - OEIS". oeis.org.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers: L(n-1) + L(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000111 (Euler or up/down numbers: e.g.f. sec(x) + tan(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 3 "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A054552 (4*n^2 - 3*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A109308 (Lesser emirps (primes whose digit reversal is a larger prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A051400 (Smallest value of x such that M(x) equals n, where M() is Mertens's function A002321)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ "}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A002445 (Denominators of Bernoulli numbers B_{2n})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001764 (binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Hadamard, J. (1893), "Résolution d'une question relative aux déterminants", Bulletin des Sciences Mathématiques, 17: 240–246
- ↑ Fujiwara, M. (2005), Introduction to Truly Beautiful Mathematics, pp. 100–101
- ↑ Sloane, N. J. A. (ed.). "Sequence A028569 (n*(n + 9))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A064410 (Number of partitions of n with zero crank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A084647 (Hypotenuses for which there exist exactly 3 distinct integer triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 4 Sloane, N. J. A. (ed.). "Sequence A065381 (Primes not of the form p + 2^k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes and k edges))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006327 (Fibonacci(n) - 3. Number of total preorders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A046931 (Prime islands: least prime whose adjacent primes are exactly 2n apart)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ 1 (to avoid n = (n-1)^1 + 1^(n-1))"}},"i":0}}]}'/>Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e., n,k > 1 (to avoid n = (n-1)^1 + 1^(n-1)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- 1 2 3 "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers: the same upside down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A045944 (Rhombic matchstick numbers: n*(3*n+2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 May 2016.
- ↑ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
- ↑ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001208 (solution to the postage stamp problem with 3 denominations and n stamps)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A000609 (Number of threshold functions of n or fewer variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ↑ Sloane, N. J. A. (ed.). "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Jon Froemke & Jerrold W. Grossman (February 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?". The American Mathematical Monthly. 100 (2). Mathematical Association of America: 180–183. doi:10.2307/2323780. JSTOR 2323780.
- ↑ Sloane, N. J. A. (ed.). "Sequence A034090 (Numbers k whose sum of proper divisors exceeds that of all smaller numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A064591 (Nonunitary perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.
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