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.

Showing 1-8 of 8 results.

A216063 a(n) is the conjectured highest power of n which has no two identical digits in succession.

Original entry on oeis.org

126, 133, 63, 32, 26, 27, 42, 33, 1, 16, 15, 11, 76, 15, 26, 19, 18, 8, 1, 45, 38, 19, 12, 16, 30, 22, 11, 21, 1, 16, 16, 11, 12, 11, 13, 10, 23, 10, 1, 22, 19, 6, 18, 25, 23, 11, 10, 6, 1, 6, 8, 20, 14, 17, 11, 13, 14, 13, 1, 15, 14, 17, 21, 16, 16, 9, 4, 11
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Comments

Contribution from Charles R Greathouse IV, Sep 17 2012: (Start)
a(n) = 0 for infinitely many n; such n have positive density in this sequence. Question: are such n of density 1?
A naive heuristic suggests that there are infinitely many n such that a(n) = 6 but only finitely many a(n) such that a(n) > 6. This suggests a weaker conjecture: this sequence is bounded. (End)

Examples

			3^133 = 2865014852390475710679572105323242035759805416923029389510561523 which has no two adjacent identical digits.

Links

Crossrefs

Cf. A043096, A216064, A216065, A215236.

Programs

  • Mathematica
    Table[mx = 0; Do[If[! MemberQ[Differences[IntegerDigits[n^k]], 0], mx = k], {k, 1000}]; mx, {n, 2, 100}] (* T. D. Noe, Sep 17 2012 *)
  • PARI
    isA043096(n)=my(v=digits(n));for(i=2,#v,if(v[i]==v[i-1],return(0)));1
a(n)=my(best=0); if(n==14,76,for(k=1, max(9,94\sqrt(log(n))), if(isA043096(n^k), best=k)); best ) \\ (conjectural) Charles R Greathouse IV, Sep 17 2012

A216064 a(n) is the conjectured highest power of n which has no three identical digits in succession.

Original entry on oeis.org

1583, 1175, 774, 1359, 776, 607, 516, 579, 2, 472, 390, 460, 812, 426, 387, 800, 502, 476, 2, 400, 472, 387, 298, 382, 466, 386, 249, 374, 2, 238, 237, 289, 243, 338, 388, 254, 189, 263, 2, 481, 442, 389, 398, 232, 412, 296, 284, 261, 2, 216, 329, 367, 341, 271, 186, 349, 340, 236
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Links

Crossrefs

Cf. A216063, A216065.

A216137 a(n) = conjectured number of integers k such that n^k has no two consecutive identical digits.

Original entry on oeis.org

40, 24, 22, 23, 10, 12, 14, 13, 1, 8, 7, 10, 10, 8, 12, 8, 6, 6, 1, 6, 6, 9, 6, 12, 8, 9, 8, 10, 1, 8, 8, 6, 5, 6, 5, 8, 8, 5, 1, 10, 5, 4, 7, 8, 6, 4, 6, 5, 1, 6, 6, 8, 7, 6, 6, 6, 4, 5, 1, 7, 5, 5, 8, 5, 4, 4, 3, 6, 1, 4, 7, 5, 5, 8, 3, 4, 5, 7, 1, 4, 6, 7, 6
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Links

Crossrefs

Cf. A216063, A216064, A216065.

Programs

  • Mathematica
    Table[cnt = 0; Do[If[! MemberQ[Differences[IntegerDigits[n^k]], 0], cnt++], {k, 1000}]; cnt, {n, 2, 100}] (* T. D. Noe, Sep 20 2012 *)

A216138 a(n) = conjectured number of integers k such that n^k has no three consecutive identical digits.

Original entry on oeis.org

335, 246, 164, 150, 141, 137, 109, 120, 2, 93, 79, 105, 105, 98, 85, 82, 76, 89, 2, 79, 79, 80, 72, 74, 71, 85, 79, 83, 2, 78, 62, 70, 76, 78, 75, 75, 67, 68, 2, 70, 70, 70, 67, 61, 65, 60, 60, 71, 2, 77, 74, 67, 63, 69, 69, 58, 62, 57, 2, 68, 60, 67, 47, 62
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Links

Crossrefs

Cf. A216063, A216064, A216065.

A216140 Conjectured number of digits in highest power of n with no two consecutive identical digits.

Original entry on oeis.org

38, 64, 38, 23, 21, 23, 38, 32, 2, 17, 17, 13, 88, 18, 32, 24, 23, 11, 2, 60, 52, 26, 17, 23, 43, 32, 16, 31, 2, 24, 25, 17, 19, 17, 21, 16, 37, 16, 2, 36, 31, 10, 30, 42, 39, 19, 17, 11, 2, 11, 14, 35, 25, 30, 20, 23, 25, 24, 2, 27, 26, 31, 38, 30, 30, 17, 8
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Comments

Number of digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012

Links

Crossrefs

Cf. A216063, A216064, A216065.

Programs

  • Mathematica
    Table[mx = 0; Do[If[! MemberQ[Differences[d = IntegerDigits[n^k]], 0], mx = Length[d]], {k, 1000}]; mx, {n, 2, 50}] (* T. D. Noe, Oct 01 2012 *)

A216141 Conjectured number of digits in highest power of n with no three consecutive identical digits.

Original entry on oeis.org

477, 561, 466, 950, 604, 513, 466, 553, 3, 492, 421, 513, 931, 502, 466, 985, 631, 609, 3, 529, 634, 527, 412, 535, 660, 553, 361, 547, 3, 355, 357, 439, 373, 522, 604, 399, 299, 419, 4, 776, 718, 636, 655, 384, 686, 495, 478, 442, 4, 369, 565, 633, 591, 472
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Comments

The number of decimal digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012

Links

Crossrefs

Cf. A216063, A216064, A216065.

A216139 a(n) = conjectured number of integers k such that n^k has no four consecutive identical digits.

Original entry on oeis.org

3674, 2385, 1836, 1608, 1438, 1333, 1239, 1201, 3, 1040, 1001, 978, 980, 948, 929, 881, 914, 852, 3, 828, 818, 834, 820, 819, 779, 786, 762, 750, 3, 708, 753, 759, 738, 676, 709, 685, 761, 703, 3, 703, 728, 707, 660, 675, 667, 633, 649, 660, 3
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Crossrefs

Cf. A216063, A216064, A216065.

A216142 Conjectured number of digits in highest power of n with no four consecutive identical digits.

Original entry on oeis.org

10797, 9347, 10797, 9858, 7550, 8503, 8031, 9347, 4, 7175, 8708, 9739, 7391, 7707, 10797, 5653, 8536, 8530, 4, 6438, 6795, 7674, 8283, 5290, 9127, 9347, 6702, 7210, 5, 7125, 7446, 10462, 7508, 8061, 7550, 6706, 5184, 7226, 5, 5934, 8607, 8624, 8663, 5484
Offset: 2

Views

Author

V. Raman, Sep 01 2012

Keywords

Comments

The number of decimal digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012

Crossrefs

Cf. A216063, A216064, A216065.
Showing 1-8 of 8 results.

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