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 21-28 of 28 results.

A245337 Sum of digits of n in fractional base 7/6.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 11, 12, 13, 14, 15, 16, 17, 15, 16, 17, 18, 19, 20, 21, 18, 19, 20, 21, 22, 23, 24, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 26, 27, 28, 29, 30
Offset: 0

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Comments

The base 7/6 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 7/6 the number 7 is represented by 60 and so a(7) = 6+0 = 6.

Links

Crossrefs

Cf. A024643, A007953, A053828.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[6 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 6) + n % 7); \\ Amiram Eldar, Jul 31 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,6,y) for y in [0..200]]

Formula

a(n) = A007953(A024643(n)). - Amiram Eldar, Jul 31 2025

A245342 Sum of digits of n written in fractional base 7/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 10, 11, 12, 13, 14, 15, 16, 7
Offset: 0

Views

Author

Hailey R. Olafson, Jul 18 2014

Keywords

Comments

The base 7/2 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 7/2 the number 14 is represented by 40 and so a(14) = 4 + 0 = 4.

Links

Crossrefs

Cf. A007953, A000120, A024639, A053828, A244040.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[2 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 2) + n % 7); \\ Amiram Eldar, Jul 31 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,2,w) for w in [0..200]]

Formula

a(n) = A007953(A024639(n)).

A245344 Sum of digits of n written in fractional base 7/3.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 11, 12, 5, 6, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 13, 14, 7, 8, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 16, 17
Offset: 0

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Comments

The base 7/3 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 7/3 the number 7 is represented by 30 and so a(7) = 3 + 0 = 3.

Links

Crossrefs

Cf. A007953, A024640, A053828, A007953.

Programs

  • Maple
    a:= proc(n) `if`(n<1, 0, irem(n, 7, 'q')+a(3*q)) end:
seq(a(n), n=0..69);  # Alois P. Heinz, May 14 2021
  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[3 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 3) + n % 7); \\ Amiram Eldar, Aug 02 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,3,y) for y in [0..200]]

Formula

a(n) = A007953(A024640(n)). - Amiram Eldar, Aug 02 2025

Extensions

Definition corrected by Georg Fischer, May 14 2021

A245349 Sum of digits of n written in fractional base 7/4.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 11, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 11, 12, 13, 14, 15, 16, 17, 12, 13, 14, 15, 16, 17, 18, 7, 8, 9, 10, 11, 12, 13, 11, 12, 13, 14, 15, 16, 17, 12, 13, 14, 15, 16, 17
Offset: 0

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Comments

The base 7/4 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 7/4 the number 7 is represented by 40 and so a(7) = 4 + 0 = 4.

Links

Crossrefs

Cf. A024641, A053828, A007953.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 4) + n % 7); \\ Amiram Eldar, Jul 31 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,4,y) for y in [0..200]]

Formula

a(n) = A007953(A024641(n)). - Amiram Eldar, Jul 31 2025

A245352 Sum of digits of n written in fractional base 7/5.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 13, 14, 9, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 19, 20, 13, 14, 15, 16, 17, 18, 19, 16, 17, 18, 19, 20, 21, 22, 13, 14, 15, 16, 17, 18, 19, 18, 19, 20, 21, 22, 23, 24, 19, 20, 21, 22, 23, 24
Offset: 0

Views

Author

Hailey R. Olafson, Jul 18 2014

Keywords

Comments

The base 7/5 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 7/5 the number 14 is represented by 530 and so a(14) = 5 + 3 + 0 = 8.

Links

Crossrefs

Cf. A007953, A000120, A244040, A024642, A053828.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[5 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 5) + n % 7); \\ Amiram Eldar, Jul 31 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,5,w) for w in [0..200]]

Formula

a(n) = A007953(A024642(n)).

A338880 Product of the nonzero digits of (n written in base 7).

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 2, 2, 4, 6, 8, 10, 12, 3, 3, 6, 9, 12, 15, 18, 4, 4, 8, 12, 16, 20, 24, 5, 5, 10, 15, 20, 25, 30, 6, 6, 12, 18, 24, 30, 36, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 2, 2, 4, 6, 8, 10, 12, 3, 3, 6, 9, 12, 15, 18, 4, 4, 8, 12
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 13 2020

Keywords

Links

Crossrefs

Cf. A007093, A051801, A053828, A117592, A309958.

Programs

  • Mathematica
    Table[Times @@ DeleteCases[IntegerDigits[n, 7], 0], {n, 0, 80}]
nmax = 80; A[] = 1; Do[A[x] = (1 + x + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6) A[x^7] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
  • PARI
    a(n) = vecprod(select(x->x, digits(n, 7))); \\ Michel Marcus, Nov 14 2020

Formula

G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6) * A(x^7).

A037327 Numbers whose base-6 and base-7 expansions have the same digit sum.

Original entry on oeis.org

1, 2, 3, 4, 5, 66, 67, 68, 69, 126, 127, 128, 129, 130, 131, 156, 157, 158, 159, 160, 189, 190, 191, 246, 247, 248, 249, 250, 251, 280, 281, 308, 309, 310, 311, 366, 367, 368, 369, 370, 396, 397, 398, 456, 457, 458, 459, 460, 461, 518, 519, 520, 521, 546, 547
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A053827, A053828.

Programs

  • PARI
    isok(k) = sumdigits(k, 6) == sumdigits(k, 7); \\ Michel Marcus, Mar 18 2023
  • Python
    from numpy import base_repr
def ok(n):
    return sum(map(int, base_repr(n, 6))) == sum(map(int, base_repr(n, 7)))
print([n for n in range(1, 10**5) if ok(n)])
# Christoph B. Kassir, Apr 05 2023

Formula

{n: A053827(n) = A053828(n)}. - R. J. Mathar, Jun 30 2021

A037331 Numbers whose base-7 and base-8 expansions have the same digit sum.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 91, 92, 93, 94, 95, 133, 134, 135, 176, 177, 178, 179, 180, 181, 217, 218, 219, 220, 221, 222, 223, 259, 260, 261, 262, 263, 304, 305, 306, 307, 385, 386, 387, 388, 389, 390, 391, 432, 433, 472, 473, 474, 475, 553
Offset: 1

Views

Author

Clark Kimberling

Keywords

Programs

  • Mathematica
    Select[Range[600],Total[IntegerDigits[#,7]]==Total[IntegerDigits[#,8]]&] (* Harvey P. Dale, Sep 05 2015 *)

Formula

{n: A053828(n) = A053829(n).} - R. J. Mathar, Jun 30 2021
Previous Showing 21-28 of 28 results.

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