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 1-3 of 3 results.

A014841 Sum modulo the base of all the digits of n in every base from 2 to n-1.

Original entry on oeis.org

0, 3, 2, 7, 6, 13, 13, 18, 19, 31, 24, 37, 40, 48, 48, 65, 59, 79, 76, 85, 93, 117, 105, 121, 132, 148, 143, 176, 163, 193, 191, 208, 226, 250, 225, 262, 277, 302, 290, 332, 320, 359, 363, 376, 394, 444, 419, 455, 462, 491, 495, 551, 540, 577, 564, 601, 625
Offset: 3

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A014836, A014837, A014838, A014839, A014840, A014842, A014843.

Programs

  • Mathematica
    Table[Sum[Mod[Total[IntegerDigits[n,i]], i], {i,2,n-1}], {n,3,59}] (* Stefano Spezia, Sep 06 2022 *)
  • PARI
    a(n) = sum(b=2, n-1, sumdigits(n, b) % b); \\ Michel Marcus, Sep 06 2022
  • Python
    from sympy.ntheory import digits
def a(n): return sum(sum(digits(n, b)[1:])%b for b in range(2, n))
print([a(n) for n in range(3, 60)]) # Michael S. Branicky, Sep 06 2022

A014840 Sum of all the digits of n in every base prime to n from 2 to n-1.

Original entry on oeis.org

2, 2, 7, 2, 15, 10, 15, 8, 34, 12, 45, 22, 31, 32, 73, 28, 90, 40, 57, 50, 135, 46, 118, 74, 117, 70, 198, 58, 222, 120, 139, 122, 192, 92, 296, 152, 216, 136, 372, 112, 408, 202, 235, 208, 497, 176, 442, 224, 338, 260, 607, 202, 454, 276, 416, 330, 755, 194, 776
Offset: 3

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A014836, A014837, A014838, A014839, A014841, A014842, A014843.

Programs

  • Maple
    f:= proc(n) local b;
 add(convert(convert(n,base,b),`+`), b = select(t -> igcd(t,n)=1, [$2..n-1]))
end proc:
map(f, [$3..100]); # Robert Israel, Nov 08 2024
  • Mathematica
    Table[Sum[If[CoprimeQ[i, n], Mod[Total[IntegerDigits[n, i]], n], 0], {i, 2, n-1}], {n, 3, 61}] (* Stefano Spezia, Sep 06 2022 *)
  • PARI
    a(n) = {s = 0; for (i=2, n-1, if (gcd(i, n) == 1, d = digits(n, i); s += sum(j=1, #d, d[j]););); s;} \\ Michel Marcus, May 30 2014
  • Python
    from math import gcd
from sympy.ntheory import digits
def a(n): return sum(sum(digits(n, b)[1:]) for b in range(2, n) if gcd(b, n) == 1)
print([a(n) for n in range(3, 62)]) # Michael S. Branicky, Sep 06 2022

A014838 Sum of all the digits of n in every prime base from 2 to n-1.

Original entry on oeis.org

2, 3, 5, 6, 9, 11, 11, 10, 14, 16, 21, 21, 21, 23, 29, 32, 39, 42, 42, 39, 47, 52, 53, 49, 52, 53, 62, 66, 76, 83, 82, 76, 77, 82, 93, 87, 85, 90, 102, 107, 120, 123, 129, 120, 134, 144, 147, 153, 150, 151, 166, 176, 178, 185, 181, 168, 184, 194, 211, 199, 207
Offset: 3

Views

Author

Olivier Gérard

Keywords

Crossrefs

Cf. A014836, A014837, A014839, A014840, A014841, A014842, A014843.

Programs

  • Mathematica
    Table[Sum[If[PrimeQ[i], Mod[Total[IntegerDigits[n, i]], n], 0], {i, 2, n-1}],{n, 3, 63}] (* Stefano Spezia, Sep 06 2022 *)
  • PARI
    a(n) = {s = 0; forprime (i=2, n-1, d = digits(n, i); s += sum(j=1, #d, d[j]);); s;} \\ Michel Marcus, May 30 2014
  • Python
    from sympy.ntheory import digits, isprime
def a(n): return sum(sum(digits(n, b)[1:]) for b in range(2, n) if isprime(b))
print([a(n) for n in range(3, 64)]) # Michael S. Branicky, Sep 06 2022
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.