# Tanya Khovanova's Sequences

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.

## My Coauthors:

• Sergei Bernstein
• Max Alekseyev
• Paul Curtz

## My Favorite Sequences:

• 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.

## My Number Gossip Sequences Related to Unique Properties of Numbers:

• 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.

## Intersection of Sequences:

• 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.

## Recursive Sequences:

• 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.

## Tracking and Non-Tracking Sequences:

• 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.

## Polyforms Sequences:

• 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.

## Operations on Sequences:

• 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).

## The Full List of Sequences:

1. 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. 2, 3, 10, 21, 55, 104, 221, 399, 782, 1595, 2759, 5328, …
A064497: Prime(n) * Fibonacci(n).
3. 2, 30, 38, 44, 74, 82, 88, 96, 106, 114, 132, 138, 140, …
A105962: Numbers n such that prime(n^2)-n is prime.
4. 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 38, 127, 408, …
A110148: Number of different tilings of a rectangle into n squares.
5. 324, 576, 784, 1296, 2304, 2500, 2704, 3136, 3600, 4356, …
A111278: Untouchable squares.
6. 10123457689, 101723, 5437, 2339, 1009, 257, 139, 173, 83, …
A112388: a(n) is the smallest prime such that a(n)^n contains every digit.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 121, 232, 272, 292, 323, 343, 434, 494, 575, 616, 737, …
A119378: Palindromic composites such that some digit permutation is prime.
14. 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.
15. 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, ...).
16. 2, 24, 311, 4062, 50153, 600240, 7000409, 80000960, 900000729, …
A119491: Sum of the first n n-digit primes.
17. 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.
18. 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.
19. 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).
20. 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).
21. 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)
22. 196, 289, 361, 441, 529, 676, 729, 841, 961, 1024, 1089, …
A119667: Squares that contain multi-digit prime substrings.
23. 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.
24. 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.
25. 35, 133, 152, 351, 370, 468, 1339, 1358, 1456, 1674, 2205, …
A120398: Sums of two distinct prime cubes..
26. 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.
27. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. 735, 3792, 1341275, 13115375, 22940075, 29373375, 71624133, …
A121342: Composite numbers that are concatenations of their distinct prime divisors.
33. 1, 2, 3, 4, 5, 6, 7, 8, 9, 54, 271, 7846, 937767, …
A121535: Numbers that are sums of substrings of their reversals.
34. 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.
35. 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.
36. 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.
37. 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.
38. 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.
39. 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.
40. 65, 145, 325, 485, 785, 901, 1025, 1157, 1445, 1765, 1937, …
A121944: Composite number of the form 4n^2+1.
41. 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).
42. 149, 198, 1392, …
A121947: Numbers that are sums of proper substrings of its reversal.
43. 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.
44. 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.
45. 1132, 1472, 1475, 1532, 1706, 1733, 1746, 1895, 1903, 2113, …
A122476: Numbers n such that n and n^3 together contain all ten digits.
46. 1807, 2396, 3257, 3698, 3908, 3968, 4073, 4554, 5307, 5670, …
A122477: Numbers n such that n and n^2 together contain all ten digits.
47. 1331, 238328, 27818127, 2815166528, 4861163384, 8972978552, …
A122659: Cubes whose digits occur exactly twice.
48. 1, 4, 9, 16, 25, 36, 49, 169, 256, 289, 1369, 13456, 13689, 134689.
A122683: Squares with increasing digits.
49. 1376, 4375, 4913, 5751, 6859, 13311, 13376, 16120, 21249, …
A122692: Cubeful numbers such that their neighbors are also cubeful.
50. 12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, …
A122726: Sociable numbers.
51. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 26, 264.
A122875: Numbers whose squares are undulating.
52. 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.
53. 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.
54. 15, 21, 34, 47, 58, 67, 88, 94, 105, 106, 107, 108, 109, …
55. 291, 979, 1411, 2059, 2419, 2491.
A123913: Semiprimes with prime factors summing up to 100.
56. 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.
57. 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.
58. 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)
59. 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.
60. 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.
61. 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.
62. 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.
63. 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.
64. 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.
65. 216, 1000, 1728, 2744, 5832, 8000, 10648, 13824, 17576, 21952, …
A124581: Abundant cubes.
66. 12, 18, 20, 24, 30, 36, 40, 48, 54, 60, 66, 72, 78, 80, …
A124626: Abundant evil numbers.
67. 1903, 2257, 2589, 2691, 2842, 2866, 3024, 3159, 3166, 3195, …
A124628: Numbers n such that n^3 is zeroless pandigital.
68. 5437, 6221, 7219, 8443, 10903, 11353, 15937, 17123, 18229, …
A124629: Primes p such that their cubes are pandigital.
69. 42, 56, 70, 84, 88, 100, 104, 112, 138, 140, 162, 168, 174, …
A124656: Abundant odious numbers.
70. 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, …
A124657: Factorials that are abundant numbers.
71. 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.
72. 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.
73. 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.
74. 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.
75. 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.
76. 10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584.
A124668: Numbers that together with their prime factors contain every digit exactly once.
77. 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).
78. 2, 3, 5, 7, 23, 25, 27, 32, 35, 37, 52, 53, 57, 72, 73, 75, …
A124673: Numbers with distinct prime digits.
79. 2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, …
A124674: Primes with distinct prime digits.
80. 1, 4, 9, 64, 81, 841, 961.
A124683: Squares with strictly decreasing digits.
81. 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.
82. 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.
83. 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.
84. 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, …
A125299: Numbers starting with a consonant.
85. 891, 941, 2931, …
A125303: Each number in this sequence is the reversal of the sum of its proper substrings.
86. 11, 88, 11, 207, 2955, …
A125304: a(n) is the smallest number such that its n power has all its digits twice.
87. 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.
88. 4, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, …
A125493: Composite deficient numbers.
89. 6, 9, 10, 12, 15, 18, 20, 24, 27, 30, 33, 34, 36, 39, 40, …
A125494: Composite evil numbers.
90. 4, 8, 14, 16, 21, 22, 25, 26, 28, 32, 35, 38, 42, 44, 49, …
A125495: Composite odious numbers.
91. 1, 8, 27, 64, 125, 343, 512, 729, 1331, 2197, 3375, 4096, …
A125496: Deficient cubes.
92. 27, 125, 216, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, …
A125497: Evil cubes.
93. 1, 8, 64, 512, 2197, 4096, 12167, 15625, 17576, 24389, 32768, …
A125498: Odious cubes.
94. 2, 4, 8, 10, 14, 16, 22, 26, 32, 34, 38, 44, 46, 50, 52, …
A125499: Deficient even numbers.
95. 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).
96. 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.
97. 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)
98. 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)
99. 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)
100. 11, 1093, 1093, 3511, 3511, 5557, 104891, …
A126197: GCD's arising in A126196. (with Max Alekseyev)
101. 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.
102. 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.
103. 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.
104. 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.
105. 256, 1296, 4096, 6561, 10000, 20736, 38416, 46656, 50625, …
A129539: Composite numbers to composite powers.
106. 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.
107. 3, 5, 9, 15, 17, 23, 27, 29, 33, 39, 43, 45, 51, 53, 57, …
A129771: Evil odd numbers.
108. 6, 12, 20, 30, 72, 90, 132, 156, 210, 240, 272, 306, 380, …
A130199: Evil oblong (pronic) numbers.
109. 3, 6, 10, 15, 36, 45, 66, 78, 105, 120, 136, 153, 190, 210, …
A130200: Evil triangular numbers.
110. 2, 42, 56, 110, 182, 342, 506, 552, 702, 812, 930, 992, …
A130201: Odious oblong (pronic) numbers.
111. 1, 21, 28, 55, 91, 171, 253, 276, 351, 406, 465, 496, 595, …
A130202: Odious triangular numbers.
112. 0, 0, 1, 2, 3, 7, 12, 28, 65, 185, …
A130616: Number of triangular polyominoes (or polyiamonds) with perimeter at most n.
113. 0, 1, 2, 5, 11, 36, 122, 538, …
A130622: Number of polyominoes with perimeter at most 2n.
114. 0, 0, 1, 1, 2, 3, 6, 8, 20, 34, 84, 182, …
A130623: Number of polyhexes with perimeter at most 2n.
115. 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.
116. 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.
117. 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.
118. 17, 197, 2041, 19879, 195226, 1920513, 18980518, …
A130817: a(n) is the total sum of the digits of n-digit primes.
119. 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.
120. 1, 2, 4, 9, 21, 56, 164, 533, 1818, 6473, 23546, 87146, …
A130866: Number of polyominoes (or square animals) with at most n cells.
121. 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).
122. 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.
123. 151, 727, 919, 10601, 14741, 15451, 15551, 16361, 16561, …
A130870: Palindromic primes with squareful neighbors.
124. 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.
125. 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.
126. 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.
127. 1, 2, 5, 12, 34, 116, 449, 1897, 8469, 38959, 182511, …
A131467: Number of planar polyhexes (A000228) with at most n cells.
128. 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.
129. 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.
130. 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.
131. 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.
132. 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.
133. 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.
134. 149, 298, 334, 472, 667, 745, 882, 1054, 1055, 1056, …
A131573: Numbers whose square starts with 3 identical digits.
135. 216, 8000, 64000, 216000, 343000, 5832000, 35937000, …
A131643: Cubes that are also sums of several consecutive cubes.
136. 6661, 16661, 26669, 46663, 56663, 66601, 66617, 66629, …
A131645: Beastly primes (primes containing 666 as a substring).
137. 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.
138. 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.
139. 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.
140. 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.
141. 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).
142. 101, 577, 677, 2203, 15877, 22501, 25609, 32401, 42061, …
A131697: Prime averages of two successive perfect prime powers.
143. 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)
144. 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.
145. 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).
146. 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).
147. 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).
148. 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).
149. 1, 10, 136, 406, 111628, 400960, 624403, 40423536, …
A133197: Triangular numbers such that moving the first digit to the end produces a square number.
150. 1, 10, 3240, 464166, 1043290, 5740966, 335936160, …
A133198: Triangular numbers such that moving the last digit to the front produces a square number.
151. 619, 16091, 19861, 61819, 116911, 119611, 160091, 169691, …
A133207: Strobogrammatic non-palindromic primes.
152. 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.
153. 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.
154. 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.
155. 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.

Revised November 2007