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 1-5 of 5 results.

A248733 Number of digits in the decimal expansion of the number of partitions of 6^n.

Original entry on oeis.org

1, 2, 5, 14, 37, 94, 236, 584, 1437, 3529, 8654, 21210, 51966, 127302, 311840, 763864, 1871094, 4583243
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Crossrefs

Cf. A129490, A248729, A248731, A248735, A077644, A248736, A248732.

Programs

  • Magma
    [Floor(Log(10,(NumberOfPartitions(6^n))))+1: n in [0..7]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    f[n_] := Floor[ Log[10, PartitionsP[ 6^n]] + 1]; Table[ f@n, {n, 0, 17}]
  • PARI
    a(n) = #Str(numbpart(6^n)); \\ Michel Marcus, Oct 16 2014
  • Python
    from sympy import npartitions
from gmpy2 import digits
def A248733(n): return len(digits(npartitions(6**n))) # Chai Wah Wu, Jul 15 2024

Formula

A248733 = A055642 o A000041 o A000400. \\ M. F. Hasler, Oct 16 2014

A248729 Number of digits in the decimal expansion of the number of partitions of 3^n.

Original entry on oeis.org

1, 1, 2, 4, 8, 15, 27, 48, 86, 152, 266, 463, 806, 1400, 2429, 4212, 7301, 12651, 21918, 37969, 65771, 113926, 197332, 341797, 592018, 1025414, 1776077
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Crossrefs

Cf. A129490, A248731, A248733, A248735, A077644, A248736, A248728.

Programs

  • Magma
    [Floor(Log(10,(NumberOfPartitions(3^n))))+1: n in [0..12]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    f[n_] := Floor[ Log[10, PartitionsP[ 3^n]] + 1]; Table[ f@n, {n, 0, 30}]
IntegerLength[PartitionsP[3^Range[0,30]]] (* Harvey P. Dale, Sep 05 2023 *)
  • PARI
    a(n) = #Str(numbpart(3^n)); \\ Michel Marcus, Oct 13 2014

Formula

a(n) = A055642(A248728(n)). - R. J. Mathar, Nov 17 2014

A248731 Number of digits in the decimal expansion of the number of partitions of 5^n.

Original entry on oeis.org

1, 1, 4, 10, 25, 58, 135, 306, 690, 1550, 3474, 7776, 17398, 38912, 87022, 194598, 435148, 973034, 2175785
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Crossrefs

Cf. A129490, A248729, A248733, A248735, A077644, A248736, A248730.

Programs

  • Magma
    [Floor(Log(10,(NumberOfPartitions(5^n))))+1: n in [0..8]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    f[n_] := Floor[ Log[10, PartitionsP[ 5^n]] + 1]; Table[ f@n, {n, 0, 30}]
IntegerLength[PartitionsP[5^Range[0,18]]] (* Harvey P. Dale, Sep 10 2021 *)
  • PARI
    a(n) = #Str(numbpart(5^n)); \\ Michel Marcus, Oct 16 2014

A248734 Number of partitions of 7^n.

Original entry on oeis.org

1, 15, 173525, 175943559810422753, 229866006383458830949778967121025947053151071434926
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Comments

Next term is too big to be included.

Crossrefs

Cf. A000041, A068413, A248728, A248730, A248732, A070177, A248735.

Programs

  • Magma
    [NumberOfPartitions(7^n): n in [0..6]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    Table[ PartitionsP[ 7^n], {n, 0, 5}]
  • PARI
    a(n) = numbpart(7^n) \\ Michel Marcus, Oct 18 2014

Formula

a(n) = A000041(7^n). - Michel Marcus, Oct 18 2014

A248736 Array, read by antidiagonals, of the numbers of digits in the decimal expansion of the number of partitions of b^n employing a conjectured formula. See both the Comments and the Mathematica coding.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 2, 4, 7, 8, 4, 1, 2, 5, 10, 15, 15, 7, 1, 2, 6, 14, 25, 32, 27, 10, 1, 2, 7, 18, 37, 58, 67, 48, 15, 1, 2, 8, 22, 51, 94, 135, 138, 86, 22, 1, 2, 9, 27, 67, 140, 236, 306, 280, 152, 32, 1, 2, 10, 32, 86, 197, 377, 584, 690, 565, 266, 47
Offset: 1

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Comments

This array is based upon the conjectured formula by Charles R Greathouse IV in A077644, adapted to other bases.
As far as the direct computations for bases b = 2..12 and powers n=0..12 cited in cross references are concerned, the values computed here conform to the exact numbers of partitions.

Examples

			\n  0  1  2  3   4   5    6    7     8     9     10     11 ...
b\
2   1  1  1  2   3   4    7   10    15    22     32     47
3   1  1  2  4   8  15   27   48    86   152    266    463
4   1  1  3  7  15  32   67  138   280   565   1134   2275
5   1  1  4 10  25  58  135  306   690  1550   3474   7776
6   1  2  5 14  37  94  236  584  1437  3529   8654  21210
7   1  2  6 18  51 140  377 1005  2668  7069  18714  49527
8   1  2  7 22  67 197  565 1607  4555 12898  36494 103238
9   1  2  8 27  86 266  806 2429  7301 21918  65771 197332
10  1  2  9 32 107 347 1108 3515 11132 35219 111391 352269
11  1  2 10 37 130 442 1476 4910 16302 54085 179401 595031
12  1  2 11 43 156 550 1918 6661 23091 80011 277190 960240

Crossrefs

Cf. A129490 (row 2), A248729 (row 3), A248731 (row 5), A248733 (row 6), A248735 (row 7), A077644 (row 10).

Programs

  • Mathematica
    f[n_, b_] := Ceiling[(Pi*Sqrt[2/3]*Sqrt[b]^n - Log[48]/2 - n*Log[b]) / Log[10]]; Table[ f[n - b, b], {n, 2, 20}, {b, n, 2, -1}] // Flatten
(* cross checked with *) g[n_, b_] := f[n, b] = Floor[ Log10[ PartitionsP[ b^n]] + 1]; Table[ f[n - b, b], {n, 2, 20}, {b, n, 2, -1}] // Flatten

Formula

a(b,n) = ceiling(Pi*sqrt(2/3)*sqrt(b)^n - log(48)/2 - n*log b) / log(10).
Showing 1-5 of 5 results.

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

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