This page describes sequences I submitted to the Online Encyclopedia of Integer Sequence (OEIS).

- My Coauthors.
- My Favorite Sequences.
- My Number Gossip Sequences Related to Unique Properties of Numbers. Many of my sequences are related to my Number Gossip page. As a part of my Number Gossip project I collect unique properties of numbers. Very often a number with a unique property can start or end a sequence. In the list of sequences related to unique properties of numbers, the number responsible for my submission of each sequence is linked to the corresponding number on my Number Gossip page.
- Intersection of Sequences. Here is how I became interested in intersections of sequences: I took my basic list of properties from my Number Gossip page and tried to analyze numbers that have two of the basic properties. I was hoping to find some unique properties of numbers and I did. For example, I found that 1 is possibly the only triangular cube. Later Max Alekseyev and Jaap Spies sent me the proof that indeed there are no triangular cubes greater than 1. While analyzing intersections, I submitted some sequences that I felt were interesting.
- Recursive Sequences. I am also interested in recursive sequences. I have a page devoted to linear Recursive Sequences of order 1 and 2, which also discusses common properties of these sequences and has some proofs. For this page I downloaded all the recursive sequences that the OEIS had at that time. There were more than a thousand of them, so I didn't want to submit many more. However, one of the sequences exemplifying the properties I discussed was missing, so I submitted it.
- Tracking and Non-tracking Sequences. I also submitted some recurrences of order higher than 2. These are related to tracking rules for radars.
- Polyforms Sequences. I am also interested in polyforms sequences. In particular, sequences related to polyiamonds, polyominoes and polyhexes. I am making a web page about these sequences. I have also submitted many polyform sequences.
- Operations on Sequences. I wrote a web page on how you can create new sequences from existing sequences. I used some of my sequences as examples for this page and I have submitted several related sequences.
- The Full List of Sequences.

- Alexey Radul
- Sergei Bernstein
- Max Alekseyev
- Paul Curtz

- 25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685,
…

A063769: Aspiring numbers: numbers whose aliquot sequence terminates in a perfect number. (with Alexey Radul) - 4, 6, 8, 9, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 42, 44,
…

A121719: Strings of digits which are composite regardless of the base in which they are interpreted. Exclude bases in which numbers are not interpretable. - 2, 17, 19, 23, 31, 53, 61, 79, 83, 107, 109, 137, 167, 173, …

A133247: Prime numbers p with property that no odd Fibonacci number is divisible by p.

- 324, 576, 784, 1296, 2304, 2500, 2704, 3136, 3600, 4356, …

A111278: Untouchable squares. - 53, 89, 107, 113, 167, 179, 251, 317, 347, 389, 397, 419, …

A119289: Prime numbers p such that there is no prime between 10*p and 10*p+9 inclusive. - 146, 206, 262, 326, 562, 626, 718, 766, 802, 818, 898, 926, …

A119379: Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number. - 80, 90, 200, 201, 202, 203, 204, 205, 206, …

A119482: Numbers that are diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...). - 196, 289, 361, 441, 529, 676, 729, 841, 961, 1024, 1089, …

A119667: Squares that contain multi-digit prime substrings. - 35, 133, 152, 351, 370, 468, 1339, 1358, 1456, 1674, 2205, …

A120398: Sums of two distinct prime cubes.. - 1692, 1809, 1902, 1908, 1920, 2019, 2079, 2169, 2190, 2673, …

A120564: Numbers n such that n together with its double and triple contain every digit. - 14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, …

A121319: a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits. - 763, 767, 1066, 1088, 1206, 1304, 1425, 1557, 1561, 1634, 1653, …

A121321: Numbers n such that every digit occurs at least once in n^4. - 309, 418, 462, 474, 575, 635, 662, 699, 702, 713, 737, 746, …

A121322: Numbers n such that n^5 contains every digit at least once. - 735, 3792, 1341275, 13115375, 22940075, 29373375, 71624133, …

A121342: Composite numbers that are concatenations of their distinct prime divisors. - 799, 889, 898, 979, 988, 997, 2779, 2797, 2977, 3499, 3949, …

A121642: Numbers with composite sum of digits and prime sum of cubes of digits. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 919, 1881, 8118, 9229, 10801, …

A121939: Palindromic numbers that contain the sum of their digits as a substring. - 1, 924, 1287, 2002, 2145, 3366, 3640, 3740, 4199, 6006, …

A121943: Numbers n such that central binomial coefficient C(2n,n) is divisible by n^2. - 65, 145, 325, 485, 785, 901, 1025, 1157, 1445, 1765, 1937, …

A121944: Composite number of the form 4n^2+1. - 149, 198, 1392, …

A121947: Numbers that are sums of proper substrings of its reversal. - 954, 1980, 2961, 3870, 5823, 7641, 9108, 19980, 29880, …

A121969: Numbers n such that if you subtract n-reversed from n you get a natural number with the same digits as n. - 459, 1467, 1692, 3285, 8019, 14967, 16992, 23706, 23769, 24894, …

A121970: Numbers n such that if you subtract n from its reversal you get a positive number with the same digits as n. - 1132, 1472, 1475, 1532, 1706, 1733, 1746, 1895, 1903, 2113, …

A122476: Numbers n such that n and n^3 together contain all ten digits. - 1807, 2396, 3257, 3698, 3908, 3968, 4073, 4554, 5307, 5670, …

A122477: Numbers n such that n and n^2 together contain all ten digits. - 1, 4, 9, 16, 25, 36, 49, 169, 256, 289, 1369, 13456, 13689, 134689.

A122683: Squares with increasing digits. - 1376, 4375, 4913, 5751, 6859, 13311, 13376, 16120, 21249, …

A122692: Cubeful numbers such that their neighbors are also cubeful. - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 26, 264.

A122875: Numbers whose squares are undulating. - 2295, 29625, 869227, …

A123911: Numbers n such that if you multiply the primes that are indexed by the digits of n and add the sum of digits of n you get n. - 291, 979, 1411, 2059, 2419, 2491.

A123913: Semiprimes with prime factors summing up to 100. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 733, …

A124107: Numbers n such that n is the sum of the augmenting factorials of the digits of n, e.g. 733 = 7 + 3! + (3!)!. (with Alexey Radul) - 216, 1000, 1728, 2744, 5832, 8000, 10648, 13824, 17576, 21952, …

A124581: Abundant cubes. - 1903, 2257, 2589, 2691, 2842, 2866, 3024, 3159, 3166, 3195, …

A124628: Numbers n such that n^3 is zeroless pandigital. - 5437, 6221, 7219, 8443, 10903, 11353, 15937, 17123, 18229, …

A124629: Primes p such that their cubes are pandigital. - 42, 56, 70, 84, 88, 100, 104, 112, 138, 140, 162, 168, 174, …

A124656: Abundant odious numbers. - 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, …

A124657: Factorials that are abundant numbers. - 5246, 5888, 7702, 7954, 9952, 9974, 10342, 10532, 11986, …

A124658: Even numbers n such that if a person is born in year n and lives not more than 100 years, then he never celebrates his prime birthday on a prime year. - 1, 2, 5, 10, 50, 101, 626, 730, 1090, 2210, 5477, 7745, 10001, …

A124664: Both n and its reverse are one more than a square. - 20, 32, 62, 84, 114, 126, 134, 135, 146, 150, 164, 168, 176, …

A124665: Numbers that cannot be either prefixed or followed by one digit to form a prime. - 487, 577, 4877, 5851, 15877, 467587, 496187, 697967, …

A124667: Prime numbers p such that the sum of the digits of p equals the sums of the digits of p^3. - 2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523.

A124674: Primes with distinct prime digits. - 1, 4, 9, 64, 81, 841, 961.

A124683: Squares with strictly decreasing digits. - 459, 1566, 2259, 2355, 11558, 12445, 111567, 112356, …

A124694: Sets of digits such that the product of the digits is 10 times the sum of the digits. Each set is arranged as a number with nondecreasing digits. - 891, 941, 2931, …

A125303: Each number in this sequence is the reversal of the sum of its proper substrings. - 11, 88, 11, 207, 2955, …

A125304: a(n) is the smallest number such that its n power has all its digits twice. - 27, 125, 216, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, …

A125497: Evil cubes. - 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 16, 17, 18, 19, 21, 22, 24, 27, 29, 32, 35, 38, 41, 59, 66, 69, 73, 75, 76, 84, 88, 93, 97, 135, 145, 203, 289, 297, 302, 319.

A129525: Numbers n such that all the digits of n^3 are distinct. - 256, 1296, 4096, 6561, 10000, 20736, 38416, 46656, 50625, …

A129539: Composite numbers to composite powers. - 252, 403, 574, 736, 765, 976, 1008, 1207, 1300, 1458, 1462, …

A129623: Numbers which are the product of a nonpalindrome and its reversal, where leading zeros are not allowed. - 17, 197, 2041, 19879, 195226, 1920513, 18980518, …

A130817: a(n) is the total sum of the digits of n-digit primes. - 158, 166, 170, 172, 178, 182, 188, 190, 196, 229, 239, 257, …

A130864: Numbers x such that x + reverse of x is a non-palindromic prime. - 151, 727, 919, 10601, 14741, 15451, 15551, 16361, 16561, …

A130870: Palindromic primes with squareful neighbors. - 149, 298, 334, 472, 667, 745, 882, 1054, 1055, 1056, …

A131573: Numbers whose square starts with 3 identical digits. - 216, 8000, 64000, 216000, 343000, 5832000, 35937000, …

A131643: Cubes that are also sums of several consecutive cubes. - 6661, 16661, 26669, 46663, 56663, 66601, 66617, 66629, …

A131645: Beastly primes (primes containing 666 as a substring). - 113, 131, 137, 173, 179, 197, 311, 313, 317, 373, 379, 419, 431, 479, 613, 617, 619, 673, 719, 797, 971, 1373, 3137, 3797, 6131, 6173, 6197, 9719.

A131648: Primes > 100 in which every multi-digit substring is also prime. - 2519, 11879, 13320, 14399, 15840, 25200, 27719, 27720, …

A131662: Numbers n where either n or n+1 is divisible by the numbers from 1 to 12. - 720, 1799, 2519, 2520, 3240, 4319, 5039, 5040, 5760, …

A131663: Numbers n where either n or n+1 is divisible by the numbers from 1 to 10. - 2420, 2421, 3602725959565.

A131759: Numbers n such that if for every digit K of n you calculate prime(K)^K and sum for all digits you get n (assumes that prime(0)^0 = 1). (with Alexey Radul) - 619, 16091, 19861, 61819, 116911, 119611, 160091, 169691, …

A133207: Strobogrammatic non-palindromic primes. - 9, 17, 19, 23, 27, 31, 45, 51, 53, 57, 61, 63, 69, 79, 81, …

A133246: Odd numbers n with property that no odd Fibonacci number is divisible by n. - 2, 17, 19, 23, 31, 53, 61, 79, 83, 107, 109, 137, 167, 173, …

A133247: Prime numbers p with property that no odd Fibonacci number is divisible by p.

- 324, 576, 784, 1296, 2304, 2500, 2704, 3136, 3600, 4356, …

A111278: Untouchable squares. - 146, 206, 262, 326, 562, 626, 718, 766, 802, 818, 898, 926, …

A119379: Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number. - 216, 1000, 1728, 2744, 5832, 8000, 10648, 13824, 17576, 21952, …

A124581: Abundant cubes. - 12, 18, 20, 24, 30, 36, 40, 48, 54, 60, 66, 72, 78, 80, …

A124626: Abundant evil numbers. - 42, 56, 70, 84, 88, 100, 104, 112, 138, 140, 162, 168, 174, …

A124656: Abundant odious numbers. - 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, …

A124657: Factorials that are abundant numbers. - 12, 20, 30, 42, 56, 72, 90, 132, 156, 210, 240, 272, 306, …

A124672: Pronic (oblong) abundant numbers = abundant numbers of the form k(k+1). - 4, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, …

A125493: Composite deficient numbers. - 6, 9, 10, 12, 15, 18, 20, 24, 27, 30, 33, 34, 36, 39, 40, …

A125494: Composite evil numbers. - 4, 8, 14, 16, 21, 22, 25, 26, 28, 32, 35, 38, 42, 44, 49, …

A125495: Composite odious numbers. - 1, 8, 27, 64, 125, 343, 512, 729, 1331, 2197, 3375, 4096, …

A125496: Deficient cubes. - 27, 125, 216, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, …

A125497: Evil cubes. - 1, 8, 64, 512, 2197, 4096, 12167, 15625, 17576, 24389, 32768, …

A125498: Odious cubes. - 2, 4, 8, 10, 14, 16, 22, 26, 32, 34, 38, 44, 46, 50, 52, …

A125499: Deficient even numbers. - 3, 5, 9, 15, 17, 23, 27, 29, 33, 39, 43, 45, 51, 53, 57, …

A129771: Evil odd numbers. - 6, 12, 20, 30, 72, 90, 132, 156, 210, 240, 272, 306, 380, …

A130199: Evil oblong (pronic) numbers. - 3, 6, 10, 15, 36, 45, 66, 78, 105, 120, 136, 153, 190, 210, …

A130200: Evil triangular numbers. - 2, 42, 56, 110, 182, 342, 506, 552, 702, 812, 930, 992, …

A130201: Odious oblong (pronic) numbers. - 1, 21, 28, 55, 91, 171, 253, 276, 351, 406, 465, 496, 595, …

A130202: Odious triangular numbers.

- 1, 4, 15, 57, 216, 819, 3105, 11772, 44631, 169209, …

A125145: a(n) = 3a(n-1) + 3a(n-2). a(0) = 1, a(1) = 4.

- 4, 10, 23, 51, 109, 228, 471, 964, 1960, 3967, 8003, 16107, …

A118645: Number of binary strings of length n+2 such that there exist 3 consecutive digits such that 2 of them are ones. - 0, 0, 1, 5, 13, 31, 71, 159, 346, 739, 1559, 3258, 6756, …

A118646: a(n) is the number of binary strings of length n such that there exists a subsequence of length 4 containing 3 or more ones. - 2, 4, 7, 11, 19, 33, 57, 97, 166, 285, 489, 838, 1436, 2462, …

A118647: a(n) is the number of binary strings of length n such that no subsequence of length 4 contains 3 or more ones. - 11, 25, 54, 114, 237, 486, 988, 1998, 4027, 8097, 16253, …

A118648: a(n) is the number of binary strings of length n+3 such that there exist a subsequence of length 4 with 2 ones in it. - 2, 4, 7, 11, 16, 26, 43, 71, 116, 186, 300, 487, 792, 1287, …

A120118: a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 3 or more ones. - 2, 4, 8, 15, 26, 48, 89, 165, 305, 561, 1034, 1908, 3521, …

A125513: a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 4 or more ones. - 0, 0, 0, 1, 6, 16, 39, 91, 207, 463, 1014, 2188, 4671, …

A130902: a(n) is the number of binary strings of length n such that there exist 4 or more ones in a subsequence of length 5 or less. - 0, 0, 1, 5, 16, 38, 85, 185, 396, 838, 1748, 3609, 7400, …

A131283: a(n) is the number of binary strings of length n such that there exist 3 or more ones in a subsequence of length 5 or less.

- 0, 0, 1, 2, 3, 7, 12, 28, 65, 185, …

A130616: Number of triangular polyominoes (or polyiamonds) with perimeter at most n. - 0, 1, 2, 5, 11, 36, 122, 538, …

A130622: Number of polyominoes with perimeter at most 2n. - 0, 0, 1, 1, 2, 3, 6, 8, 20, 34, 84, 182, …

A130623: Number of polyhexes with perimeter at most 2n. - 1, 2, 4, 9, 21, 56, 164, 533, 1818, 6473, 23546, 87146, …

A130866: Number of polyominoes (or square animals) with at most n cells. - 1, 2, 3, 6, 10, 22, 46, 112, 272, 720, 1906, 5240, 14475, …

A130867: Triangular polyominoes (or polyiamonds) with n cells at most (turning over is allowed, holes are allowed, must be connected along edges). - 1, 2, 5, 12, 34, 116, 449, 1897, 8469, 38959, 182511, …

A131467: Number of planar polyhexes (A000228) with at most n cells. - 1, 1, 1, 3, 4, 11, 23, 62, 149, 409, 1066, 2931, 7981, …

A131481: a(n) is the number of n-cell polyiamonds (triangular polyominoes) with perimeter n+2. - 1, 1, 2, 4, 11, 27, 83, 255, 847, 2829, 9734, 33724, …

A131482: a(n) is the number of n-celled polyominoes with perimeter 2n+2. - 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 4, 1, 11, 1, 23, 4, 62, 11, …

A131486: a(n) is the number of triangular polyominoes (polyiamonds) with n edges. - 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 4, 0, 1, 11, 1, 7, 27, …

A131487: a(n) is the number of polyominoes with n edges. - 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, …

A131488: a(n) is the number of polyhexes with n edges.

- 2, 3, 10, 21, 55, 104, 221, 399, 782, 1595, 2759, 5328, …

A064497: Prime(n) * Fibonacci(n). - 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, …

A129344: a(n) is the number of n-digit powers of 2. - 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

A130713: a(0)=a(2)=1, a(1)=2, a(n)=0 for n>2. - 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

A130716: a(0)=a(1)=a(2)=1, a(n)=0 for n>2. - 1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, …

A131234: Starts with 1, then n appears Fibonacci(n-1) times. - 0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, …

A131511: All possible products of prime and Fibonacci numbers. - 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, …

A132147: Numbers that can be presented as a sum of a prime number and a Fibonacci number. (0 is not considered a Fibonacci number).

- 25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685, …

A063769: Aspiring numbers: numbers whose aliquot sequence terminates in a perfect number. (with Alexey Radul) - 2, 3, 10, 21, 55, 104, 221, 399, 782, 1595, 2759, 5328, …

A064497: Prime(n) * Fibonacci(n). - 2, 30, 38, 44, 74, 82, 88, 96, 106, 114, 132, 138, 140, …

A105962: Numbers n such that prime(n^2)-n is prime. - 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 38, 127, 408, …

A110148: Number of different tilings of a rectangle into n squares. - 324, 576, 784, 1296, 2304, 2500, 2704, 3136, 3600, 4356, …

A111278: Untouchable squares. - 10123457689, 101723, 5437, 2339, 1009, 257, 139, 173, 83, …

A112388: a(n) is the smallest prime such that a(n)^n contains every digit. - 4, 10, 23, 51, 109, 228, 471, 964, 1960, 3967, 8003, 16107, …

A118645: Number of binary strings of length n+2 such that there exist 3 consecutive digits such that 2 of them are ones. - 0, 0, 1, 5, 13, 31, 71, 159, 346, 739, 1559, 3258, 6756, …

A118646: a(n) is the number of binary strings of length n such that there exists a subsequence of length 4 containing 3 or more ones. - 2, 4, 7, 11, 19, 33, 57, 97, 166, 285, 489, 838, 1436, 2462, …

A118647: a(n) is the number of binary strings of length n such that no subsequence of length 4 contains 3 or more ones. - 11, 25, 54, 114, 237, 486, 988, 1998, 4027, 8097, 16253, …

A118648: a(n) is the number of binary strings of length n+3 such that there exist a subsequence of length 4 with 2 ones in it. - 53, 89, 107, 113, 167, 179, 251, 317, 347, 389, 397, 419, …

A119289: Prime numbers p such that there is no prime between 10*p and 10*p+9 inclusive. - 9, 18, 27, 31, 22, 31, 40, 49, 33, 24, 33, 42, 51, 55, 46, …

A119310: Alphabetical value of n in its Roman numerals-based representation. - 121, 232, 272, 292, 323, 343, 434, 494, 575, 616, 737, …

A119378: Palindromic composites such that some digit permutation is prime. - 146, 206, 262, 326, 562, 626, 718, 766, 802, 818, 898, 926, …

A119379: Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number. - 80, 90, 200, 201, 202, 203, 204, 205, 206, …

A119482: Numbers that are diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...). - 2, 24, 311, 4062, 50153, 600240, 7000409, 80000960, 900000729, …

A119491: Sum of the first n n-digit primes. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, …

A119509: Numbers whose squares contain all different digits. - 1, 15, 149, 2357, 10541, 57735, 745356, 1490712, 182574186, …

A119511: a(n) is the smallest positive integer whose square starts with precisely n identical digits. - 4, 10, 20, 34, 52, 73, 96, 120, 144, 168, 192, 216, 240, 264, …

A119651: Number of different values of exactly n standard American coins (pennies, nickels, dimes and quarters). - 4, 13, 27, 46, 69, 94, 119, 144, 169, 194, 219, 244, 269, 294, 319, …

A119652: Number of different values of ≤ n standard American coins (pennies, nickels, dimes and quarters). - 2, 8, 98, 3624, 632148, …

A119654: a(n) is the smallest number that starts a consecutive block of n numbers with at least n prime divisors (counting multiplicity) each. (with Alexey Radul) - 196, 289, 361, 441, 529, 676, 729, 841, 961, 1024, 1089, …

A119667: Squares that contain multi-digit prime substrings. - 1, 15, 149, 2357, 10541, 57735, 745356, 1490712, 182574186, …

A119998: a(n) is the smallest positive integer whose square starts with (at least) n identical digits. - 2, 4, 7, 11, 16, 26, 43, 71, 116, 186, 300, 487, 792, 1287, …

A120118: a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 3 or more ones. - 35, 133, 152, 351, 370, 468, 1339, 1358, 1456, 1674, 2205, …

A120398: Sums of two distinct prime cubes.. - 1692, 1809, 1902, 1908, 1920, 2019, 2079, 2169, 2190, 2673, …

A120564: Numbers n such that n together with its double and triple contain every digit. - 0, 0, 0, 0, 2, 11, 41, 136, 437, 1397, 4490, 14554, 47683, …

A121244: Number of score vectors for tournaments on n nodes that do not determine the tournament uniquely. - 0, 0, 0, 0, 5, 45, 438, 6849, 191483, 9732967, 903753099, …

A121272: Number of outcomes of unlabeled n-team round-robin tournaments that are not uniquely defined by their score vectors. - 14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, …

A121319: a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits. - 763, 767, 1066, 1088, 1206, 1304, 1425, 1557, 1561, 1634, 1653, …

A121321: Numbers n such that every digit occurs at least once in n^4. - 309, 418, 462, 474, 575, 635, 662, 699, 702, 713, 737, 746, …

A121322: Numbers n such that n^5 contains every digit at least once. - 735, 3792, 1341275, 13115375, 22940075, 29373375, 71624133, …

A121342: Composite numbers that are concatenations of their distinct prime divisors. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 54, 271, 7846, 937767, …

A121535: Numbers that are sums of substrings of their reversals. - 27, 45, 54, 72, 78, 87, 126, 159, 162, 168, 186, 195, 207, …

A121614: Numbers n that have composite sum of digits and prime sum of squares of digits. - 799, 889, 898, 979, 988, 997, 2779, 2797, 2977, 3499, 3949, …

A121642: Numbers with composite sum of digits and prime sum of cubes of digits. - 4, 6, 8, 9, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 42, 44, …

A121719: Strings of digits which are composite regardless of the base in which they are interpreted. Exclude bases in which numbers are not interpretable. - 2, 588, 864, 2430, 7776, 27000, 55296, 69984, 82134, 215622, …

A121850: Numbers n such that (phi(n) + sigma(n))/(rad(n))^2 is an integer, that is (phi(n) + sigma(n)) is divisible by every prime factor of n squared. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 919, 1881, 8118, 9229, 10801, …

A121939: Palindromic numbers that contain the sum of their digits as a substring. - 1, 924, 1287, 2002, 2145, 3366, 3640, 3740, 4199, 6006, …

A121943: Numbers n such that central binomial coefficient C(2n,n) is divisible by n^2. - 65, 145, 325, 485, 785, 901, 1025, 1157, 1445, 1765, 1937, …

A121944: Composite number of the form 4n^2+1. - 1, 3, 11, 69, 929, 30273, 2591057, 614059329, 423463272449, …

A121945: a(n) is the sum of the first n factorials in decreasing powers from n to 1. a(n) = Sum_{k = 1..n} k!^(n-k+1). - 149, 198, 1392, …

A121947: Numbers that are sums of proper substrings of its reversal. - 954, 1980, 2961, 3870, 5823, 7641, 9108, 19980, 29880, …

A121969: Numbers n such that if you subtract n-reversed from n you get a natural number with the same digits as n. - 459, 1467, 1692, 3285, 8019, 14967, 16992, 23706, 23769, 24894, …

A121970: Numbers n such that if you subtract n from its reversal you get a positive number with the same digits as n. - 1132, 1472, 1475, 1532, 1706, 1733, 1746, 1895, 1903, 2113, …

A122476: Numbers n such that n and n^3 together contain all ten digits. - 1807, 2396, 3257, 3698, 3908, 3968, 4073, 4554, 5307, 5670, …

A122477: Numbers n such that n and n^2 together contain all ten digits. - 1331, 238328, 27818127, 2815166528, 4861163384, 8972978552, …

A122659: Cubes whose digits occur exactly twice. - 1, 4, 9, 16, 25, 36, 49, 169, 256, 289, 1369, 13456, 13689, 134689.

A122683: Squares with increasing digits. - 1376, 4375, 4913, 5751, 6859, 13311, 13376, 16120, 21249, …

A122692: Cubeful numbers such that their neighbors are also cubeful. - 12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, …

A122726: Sociable numbers. - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 26, 264.

A122875: Numbers whose squares are undulating. - 71, 37, 131, 251, 199, 79, 139, 1151, 827, 89, 71, 107, 467, …

A122967: Greatest prime factor of the pair of amicable numbers. Amicable numbers are sorted by the smaller number in the pair. - 2295, 29625, 869227, …

A123911: Numbers n such that if you multiply the primes that are indexed by the digits of n and add the sum of digits of n you get n. - 15, 21, 34, 47, 58, 67, 88, 94, 105, 106, 107, 108, 109, …

A123912: Numbers whose squares start with 2 identical digits. - 291, 979, 1411, 2059, 2419, 2491.

A123913: Semiprimes with prime factors summing up to 100. - 1, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, …

A123976: Numbers n such that Fibonacci(n-1) is divisible by n. - 1, 7, 13, 19, 23, 28, 44, 49, 68, 79, 129, 133, 139, 167, …

A124095: Happy numbers without zeros and with digits in non-decreasing order. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 733, …

A124107: Numbers n such that n is the sum of the augmenting factorials of the digits of n, e.g. 733 = 7 + 3! + (3!)!. (with Alexey Radul) - 0, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 1, …

A124210: a(n) is the number of positive integers k such that sum of digits of 2^k equals n. - 2, 158, 192, 216, 356, 426, 548, 680, 1178, 1196, 1466, …

A124225: Numbers n such that the sum of the first n primes is prime as well as the sum of the squares of the first n primes is prime. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, …

A124231: Numbers n such that pi(n) is palindromic, where pi(n) is the number of primes less than or equal to n. - 1, 2, 3, 4, 5, 26, 32, 36, 138, 3691, 6987, 7193, 86969, …

A124232: Numbers n such that prime(n) and pi(n) are palindromic. - 15, 17, 21, 27, 31, 45, 51, 63, 65, 73, 85, 93, 107, 119, …

A124334: Nonpalindromes in base 10 that are palindromes in base 2. - 10, 12, 13, 14, 16, 18, 19, 20, 23, 24, 25, 26, 28, 29, 30, …

A124404: Nonpalindromes in base 10 that are nonpalindromes in base 2. - 216, 1000, 1728, 2744, 5832, 8000, 10648, 13824, 17576, 21952, …

A124581: Abundant cubes. - 12, 18, 20, 24, 30, 36, 40, 48, 54, 60, 66, 72, 78, 80, …

A124626: Abundant evil numbers. - 1903, 2257, 2589, 2691, 2842, 2866, 3024, 3159, 3166, 3195, …

A124628: Numbers n such that n^3 is zeroless pandigital. - 5437, 6221, 7219, 8443, 10903, 11353, 15937, 17123, 18229, …

A124629: Primes p such that their cubes are pandigital. - 42, 56, 70, 84, 88, 100, 104, 112, 138, 140, 162, 168, 174, …

A124656: Abundant odious numbers. - 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, …

A124657: Factorials that are abundant numbers. - 5246, 5888, 7702, 7954, 9952, 9974, 10342, 10532, 11986, …

A124658: Even numbers n such that if a person is born in year n and lives not more than 100 years, then he never celebrates his prime birthday on a prime year. - 1, 2, 5, 10, 50, 101, 626, 730, 1090, 2210, 5477, 7745, 10001, …

A124664: Both n and its reverse are one more than a square. - 20, 32, 62, 84, 114, 126, 134, 135, 146, 150, 164, 168, 176, …

A124665: Numbers that cannot be either prefixed or followed by one digit to form a prime. - 891, 921, 1029, 1037, 1653, 1763, 1857, 2427, 2513, 2519, …

A124666: Numbers ending in 1, 3, 7 or 9 such that either prepending or following them by one digit doesn't produce a prime. - 487, 577, 4877, 5851, 15877, 467587, 496187, 697967, …

A124667: Prime numbers p such that the sum of the digits of p equals the sums of the digits of p^3. - 10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584.

A124668: Numbers that together with their prime factors contain every digit exactly once. - 12, 20, 30, 42, 56, 72, 90, 132, 156, 210, 240, 272, 306, …

A124672: Pronic (oblong) abundant numbers = abundant numbers of the form k(k+1). - 2, 3, 5, 7, 23, 25, 27, 32, 35, 37, 52, 53, 57, 72, 73, 75, …

A124673: Numbers with distinct prime digits. - 2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, …

A124674: Primes with distinct prime digits. - 1, 4, 9, 64, 81, 841, 961.

A124683: Squares with strictly decreasing digits. - 459, 1566, 2259, 2355, 11558, 12445, 111567, 112356, …

A124694: Sets of digits such that the product of the digits is 10 times the sum of the digits. Each set is arranged as a number with nondecreasing digits. - 1, 4, 15, 57, 216, 819, 3105, 11772, 44631, 169209, …

A125145: a(n) = 3a(n-1) + 3a(n-2). a(0) = 1, a(1) = 4. - 1, 5, 6, 7, 8, 9, 15, 16, 19, 23, 39, 53, 74, 92, …

A125298: Atomic numbers of elements having a single letter chemical symbol. - 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, …

A125299: Numbers starting with a consonant. - 891, 941, 2931, …

A125303: Each number in this sequence is the reversal of the sum of its proper substrings. - 11, 88, 11, 207, 2955, …

A125304: a(n) is the smallest number such that its n power has all its digits twice. - 4, 25, 76, 125, 187, 255, 437, 629, 1152, 1276, 1298, 1352, …

A125309: Numbers n such that twice the sum of the prime factors of n equals the product of the digits of n. - 4, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, …

A125493: Composite deficient numbers. - 6, 9, 10, 12, 15, 18, 20, 24, 27, 30, 33, 34, 36, 39, 40, …

A125494: Composite evil numbers. - 4, 8, 14, 16, 21, 22, 25, 26, 28, 32, 35, 38, 42, 44, 49, …

A125495: Composite odious numbers. - 1, 8, 27, 64, 125, 343, 512, 729, 1331, 2197, 3375, 4096, …

A125496: Deficient cubes. - 27, 125, 216, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, …

A125497: Evil cubes. - 1, 8, 64, 512, 2197, 4096, 12167, 15625, 17576, 24389, 32768, …

A125498: Odious cubes. - 2, 4, 8, 10, 14, 16, 22, 26, 32, 34, 38, 44, 46, 50, 52, …

A125499: Deficient even numbers. - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 18, 19, 21, 23, 24, …

A125506: Numbers with distinct digits in reverse alphabetical order (in English). - 2, 4, 8, 15, 26, 48, 89, 165, 305, 561, 1034, 1908, 3521, …

A125513: a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 4 or more ones. - 3, 75, 825, 8835, 89235, 898335, 8992335, 89983335, 899923335, …

A125520: a(n) = maximal difference between two distinct n-digit with property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen. (with Sergei Bernstein) - 3, 6, 30, 60, 300, 600, 3000, 6000, 30000, 60000, …

A125521: a(n) = minimal difference between two distinct n-digit with property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen. (with Sergei Bernstein) - 7, 546, 1092, 1755, 3510, 4896, 52447, …

A126196: Numbers n such that gcd(numerator(H(n)),numerator(H([n/2]))) > 1, where H() are the harmonic numbers. (with Max Alekseyev) - 11, 1093, 1093, 3511, 3511, 5557, 104891, …

A126197: GCD's arising in A126196. (with Max Alekseyev) - 5, 6, 12, 20, 24, 32, 64, 69, 70, 80, 82, 98, 129, 148, …

A126593: Numbers that belong to a cycle under the map k = Sum d_i 10^i -> f(k) = Sum d_i 2^i. - 1, 36, 66, 88, 257, 268, 279, 448, 369, 459, 0, 666, 0, …

A126789: a(n) is the smallest number such that the product of its digits is n times the sum of its digits, or 0 if no such number exists. - 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, …

A129344: a(n) is the number of n-digit powers of 2. - 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 16, 17, 18, 19, 21, 22, …

A129525: Numbers n such that all the digits of n^3 are distinct. - 256, 1296, 4096, 6561, 10000, 20736, 38416, 46656, 50625, …

A129539: Composite numbers to composite powers. - 252, 403, 574, 736, 765, 976, 1008, 1207, 1300, 1458, 1462, …

A129623: Numbers which are the product of a nonpalindrome and its reversal, where leading zeros are not allowed. - 3, 5, 9, 15, 17, 23, 27, 29, 33, 39, 43, 45, 51, 53, 57, …

A129771: Evil odd numbers. - 6, 12, 20, 30, 72, 90, 132, 156, 210, 240, 272, 306, 380, …

A130199: Evil oblong (pronic) numbers. - 3, 6, 10, 15, 36, 45, 66, 78, 105, 120, 136, 153, 190, 210, …

A130200: Evil triangular numbers. - 2, 42, 56, 110, 182, 342, 506, 552, 702, 812, 930, 992, …

A130201: Odious oblong (pronic) numbers. - 1, 21, 28, 55, 91, 171, 253, 276, 351, 406, 465, 496, 595, …

A130202: Odious triangular numbers. - 0, 0, 1, 2, 3, 7, 12, 28, 65, 185, …

A130616: Number of triangular polyominoes (or polyiamonds) with perimeter at most n. - 0, 1, 2, 5, 11, 36, 122, 538, …

A130622: Number of polyominoes with perimeter at most 2n. - 0, 0, 1, 1, 2, 3, 6, 8, 20, 34, 84, 182, …

A130623: Number of polyhexes with perimeter at most 2n. - 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

A130713: a(0)=a(2)=1, a(1)=2, a(n)=0 for n>2. - 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

A130716: a(0)=a(1)=a(2)=1, a(n)=0 for n>2. - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …

A130734: List of numbers of cents you can have in US coins without having change for a dollar. - 17, 197, 2041, 19879, 195226, 1920513, 18980518, …

A130817: a(n) is the total sum of the digits of n-digit primes. - 158, 166, 170, 172, 178, 182, 188, 190, 196, 229, 239, 257, …

A130864: Numbers x such that x + reverse of x is a non-palindromic prime. - 1, 2, 4, 9, 21, 56, 164, 533, 1818, 6473, 23546, 87146, …

A130866: Number of polyominoes (or square animals) with at most n cells. - 1, 2, 3, 6, 10, 22, 46, 112, 272, 720, 1906, 5240, 14475, …

A130867: Triangular polyominoes (or polyiamonds) with n cells at most (turning over is allowed, holes are allowed, must be connected along edges). - 13, 157, 436, 515, 847, 863, 900, 913, 987, 992, 1010, …

A130868: Numbers n such that the set of integer digits of n^2 is the same as of (n+1)^2. - 151, 727, 919, 10601, 14741, 15451, 15551, 16361, 16561, …

A130870: Palindromic primes with squareful neighbors. - 0, 0, 0, 1, 6, 16, 39, 91, 207, 463, 1014, 2188, 4671, …

A130902: a(n) is the number of binary strings of length n such that there exist 4 or more ones in a subsequence of length 5 or less. - 1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, …

A131234: Starts with 1, then n appears Fibonacci(n-1) times. - 0, 0, 1, 5, 16, 38, 85, 185, 396, 838, 1748, 3609, 7400, …

A131283: a(n) is the number of binary strings of length n such that there exist 3 or more ones in a subsequence of length 5 or less. - 1, 2, 5, 12, 34, 116, 449, 1897, 8469, 38959, 182511, …

A131467: Number of planar polyhexes (A000228) with at most n cells. - 1, 1, 1, 3, 4, 11, 23, 62, 149, 409, 1066, 2931, 7981, …

A131481: a(n) is the number of n-cell polyiamonds (triangular polyominoes) with perimeter n+2. - 1, 1, 2, 4, 11, 27, 83, 255, 847, 2829, 9734, 33724, …

A131482: a(n) is the number of n-celled polyominoes with perimeter 2n+2. - 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 4, 1, 11, 1, 23, 4, 62, 11, …

A131486: a(n) is the number of triangular polyominoes (polyiamonds) with n edges. - 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 4, 0, 1, 11, 1, 7, 27, …

A131487: a(n) is the number of polyominoes with n edges. - 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, …

A131488: a(n) is the number of polyhexes with n edges. - 0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, …

A131511: All possible products of prime and Fibonacci numbers. - 149, 298, 334, 472, 667, 745, 882, 1054, 1055, 1056, …

A131573: Numbers whose square starts with 3 identical digits. - 216, 8000, 64000, 216000, 343000, 5832000, 35937000, …

A131643: Cubes that are also sums of several consecutive cubes. - 6661, 16661, 26669, 46663, 56663, 66601, 66617, 66629, …

A131645: Beastly primes (primes containing 666 as a substring). - 30, 70, 105, 231, 286, 627, 646, 805, 897, 1122, 1581, …

A131647: Numbers that are products of distinct primes and divisible by the sum of those primes. - 113, 131, 137, 173, 179, 197, 311, 313, 317, 373, 379, 419, 431, 479, 613, 617, 619, 673, 719, 797, 971, 1373, 3137, 3797, 6131, 6173, 6197, 9719.

A131648: Primes > 100 in which every multi-digit substring is also prime. - 2519, 11879, 13320, 14399, 15840, 25200, 27719, 27720, …

A131662: Numbers n where either n or n+1 is divisible by the numbers from 1 to 12. - 720, 1799, 2519, 2520, 3240, 4319, 5039, 5040, 5760, …

A131663: Numbers n where either n or n+1 is divisible by the numbers from 1 to 10. - 101, 103, 107, 109, 113, 127, 131, 211, 223, 227, 229, …

A131687: Days of the year that are prime numbers in format mmdd (2-digit month followed by 2-digit year). - 101, 577, 677, 2203, 15877, 22501, 25609, 32401, 42061, …

A131697: Prime averages of two successive perfect prime powers. - 2420, 2421, 3602725959565.

A131759: Numbers n such that if for every digit K of n you calculate prime(K)^K and sum for all digits you get n (assumes that prime(0)^0 = 1). (with Alexey Radul) - 1, 4, 9, 121, 484, 676, 2178, 8712, 10000, 10201, 12321, …

A131760: Numbers n such that n multiplied by its reverse yields a fourth power. - 1, 35, 119, 125, 177, 208, 209, 221, 255, 287, 299, 329, …

A132144: Numbers that can't be presented as a sum of a prime number and a Fibonacci number. (0 is considered a Fibonacci number). - 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, …

A132145: Numbers that can be presented as a sum of a prime number and a Fibonacci number. (0 is considered a Fibonacci number). - 1, 2, 17, 29, 35, 59, 83, 89, 119, 125, 127, 177, 179, …

A132146: Numbers that can't be presented as a sum of a prime number and a Fibonacci number. (0 is not considered a Fibonacci number). - 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, …

A132147: Numbers that can be presented as a sum of a prime number and a Fibonacci number. (0 is not considered a Fibonacci number). - 1, 10, 136, 406, 111628, 400960, 624403, 40423536, …

A133197: Triangular numbers such that moving the first digit to the end produces a square number. - 1, 10, 3240, 464166, 1043290, 5740966, 335936160, …

A133198: Triangular numbers such that moving the last digit to the front produces a square number. - 619, 16091, 19861, 61819, 116911, 119611, 160091, 169691, …

A133207: Strobogrammatic non-palindromic primes. - 12, 5, 4, 348, …

A133208: a(n) is the smallest number k such that k^n has the same digits as some other n-th power without leading zeroes. - 1, 125874, 1035, 1782, 142857, 1386, 1359, 113967, 1089.

A133220: a(n) is the smallest number k such that k and n*k are anagrams. - 9, 17, 19, 23, 27, 31, 45, 51, 53, 57, 61, 63, 69, 79, 81, …

A133246: Odd numbers n with property that no odd Fibonacci number is divisible by n. - 2, 17, 19, 23, 31, 53, 61, 79, 83, 107, 109, 137, 167, 173, …

A133247: Prime numbers p with property that no odd Fibonacci number is divisible by p.

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Revised November 2007