cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 31-37 of 37 results.

A035254 First differences of A035253.

Original entry on oeis.org

-3, -1, 1, 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64
Offset: 0

Views

Author

Robet Bronson (bob(AT)bronsons.com)

Keywords

Crossrefs

Different from A030124. Cf. A002024, A014132, A014133. First differences are in A035214.

Programs

  • Python
    from math import isqrt
def A035254(n): return n+(isqrt(n<<3)-5>>1) # Chai Wah Wu, Jun 07 2025

Formula

a(n) = A002024(n)+n-3. - Chai Wah Wu, Jun 07 2025

A056738 Positions where 2's occur in A056731.

Original entry on oeis.org

1, 4, 8, 13, 20, 28, 37, 47, 59, 72, 86, 101, 117, 135, 154, 174, 195, 217, 240, 264, 290, 317, 345, 374, 404, 435, 467, 500, 535, 571, 608, 646, 685, 725, 766, 808, 851, 896, 942, 989, 1037, 1086, 1136, 1187, 1239, 1292, 1346, 1402, 1459, 1517, 1576, 1636
Offset: 1

Views

Author

N. J. A. Sloane, Aug 31 2000

Keywords

Examples

			a(9) = a(8) + 8 + the number of a(k)'s <= 8 = 47 + 8 + 1 + 3 ( a(3) is <= 8) = 59.

Programs

  • Mathematica
    f[1] = 1; f[n_] := f[n] = Block[ {k = 1}, While[ f[k] < n, k++ ]; Return[ f[n - 1] + n + k ]]; Table[ f[n], {n, 0, 60} ]

Formula

A056738(n) = A005228(n)+A030124(n)-n-1.
a(n+1) = a(n) + (n+1) + the number of a(k)'s <= n, 1 <= k <= n and a(1) = 1.

Extensions

More terms from Robert G. Wilson v, Nov 25 2001

A081689 A005228 - 1.

Original entry on oeis.org

0, 2, 6, 11, 17, 25, 34, 44, 55, 68, 82, 97, 113, 130, 149, 169, 190, 212, 235, 259, 284, 311, 339, 368, 398, 429, 461, 494, 528, 564, 601, 639, 678, 718, 759, 801, 844, 888, 934, 981, 1029, 1078, 1128, 1179, 1231, 1284, 1338, 1393, 1450, 1508, 1567, 1627, 1688
Offset: 0

Views

Author

N. J. A. Sloane, Apr 02 2003

Keywords

Comments

From P-positions in a certain game.

Links

Crossrefs

Cf. A030124, A005228, A081688.

Formula

See A081688 for a recurrence.

A139310 Has two properties: concatenation of its digits is same string as concatenation of digits of its first differences and every number appears exactly one of the sequence or its first differences.

Original entry on oeis.org

1, 12, 14, 155, 160, 211, 271, 292, 419, 548, 572, 591, 645, 653, 710, 735, 744, 760, 764, 820, 873, 880, 890, 963, 1537, 1584, 2191, 2197, 2245, 2265, 2352, 2355, 11163, 11253, 11349, 11380, 11917, 11932, 12016, 12235, 12356, 12453, 12475, 12520, 12746
Offset: 1

Views

Author

N. J. A. Sloane (based on Angelini's article), Jun 08 2008

Keywords

Comments

When there is a choice in choosing the next term in the first differences, choose the smallest number not yet present in either the sequence or its first differences.

References

  • E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Links

Crossrefs

Cf. A139311 (first differences), A005228, A030124.

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010
Correction to a(12) and more terms from Jon E. Schoenfield, May 23 2010

A274688 First differences of A274687.

Original entry on oeis.org

-2, 3, -5, 7, -8, 9, -11, 12, -13, 15, -17, 19, -20, 21, -23, 25, -27, 28, -29, 31, -32, 33, -35, 36, -37, 39, -41, 43, -44, 45, -47, 48, -49, 51, -52, 53, -55, 57, -59, 60, -61, 63, -65, 67, -68, 69, -71, 73, -75, 76, -77, 79, -80, 81, -83, 84, -85, 87, -89
Offset: 1

Views

Author

Max Barrentine, Jul 02 2016

Keywords

Comments

This sequence and its partial sums plus one list every integer except zero.

Crossrefs

Cf. A030124, A053661, A274687.

Formula

If n is even, a(n) = A053661(n+1); if n is odd, a(n) = -A053661(n+1)

A274690 First differences of A274689.

Original entry on oeis.org

-2, 3, 4, 5, -3, 7, -5, 9, -6, 12, -4, -7, 16, -8, 17, -10, -9, 18, -11, 23, -13, 24, -12, -14, 28, -15, -16, 26, -17, 31, -18, -20, 33, -21, 36, -22, 40, -19, -24, 42, -23, -25, 43, -26, 44, -27, -29, 45, -28, 47, -30, -31, 52, -32, 53, -34, -33, 62, -35, -37
Offset: 1

Views

Author

Max Barrentine, Jul 02 2016

Keywords

Comments

It appears that this sequence and its partial sums plus one list every integer except zero.

Crossrefs

Cf. A030124, A274689.

A109592 Sequence and first differences include all even numbers exactly once and no odd numbers.

Original entry on oeis.org

2, 6, 14, 24, 36, 52, 70, 90, 112, 138, 166, 196, 228, 262, 300, 340, 382, 426, 472, 520, 570, 624, 680, 738, 798, 860, 924, 990, 1058, 1130, 1204, 1280, 1358, 1438, 1520, 1604, 1690, 1778, 1870, 1964, 2060, 2158, 2258, 2360, 2464, 2570, 2678, 2788, 2902
Offset: 1

Views

Author

Eric Angelini, Aug 30 2005

Keywords

Comments

First differences = 2*A030124.

References

  • E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Crossrefs

Cf. A005228, A030124.

Formula

a(n) = 2*A005228(n).

Extensions

Edited, corrected and extended by Ray Chandler, Sep 06 2005
Previous Showing 31-37 of 37 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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