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 1-10 of 14 results. Next

A111364 Index of first occurrence of n in A033093 (or 0 if not present).

Original entry on oeis.org

1, 2, 5, 4, 22, 8, 12, 27, 16, 18, 50, 32, 54, 36, 66, 64, 100, 84, 72, 132, 128, 200, 168, 280, 144, 252, 270, 264, 300, 288, 360, 528, 600, 504, 780, 1040, 540, 1026, 1092, 840, 720, 1152, 900, 1320, 1296, 2184, 1260, 1080, 1680, 2376, 2340, 3150, 2304, 1800
Offset: 0

Views

Author

Franklin T. Adams-Watters, Nov 07 2005

Keywords

Comments

Conjecture that the sequence contains no zeros; that is, A033093 is onto the nonnegative integers. Note that most of the values in the sequence are highly divisible, as would expected. a(7) appears to be the last odd value.

Examples

			a(7)=27 because A033093(27)=7 and no smaller n has A033093(n)=7.

Crossrefs

Cf. A033093.

A033107 Number of 7's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 4, 3, 4, 2, 5, 3, 6, 3, 3, 2, 7, 2, 3, 5, 6, 3, 5, 2, 4, 3, 6, 3, 9, 2, 3, 4, 4, 4, 6, 3, 8, 4, 3, 2
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A033093, A033095, A033097, A033099, A033101, A033103, A033105, A033108, A033109, A033111.

Programs

  • Maple
    f:= proc(n) local b;`+`(seq(numboccur(7,convert(n,base,b)),b=8..n+1)) end proc:
map(f, [$1..100]); # Robert Israel, Aug 20 2024
  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 7]; Array[f, 90] (* Robert G. Wilson v, Nov 14 2012 *)

A033094 Number of 0's when k is written in base b for all b and k satisfying 2<=b<=n+1, 1<=k<=n.

Original entry on oeis.org

0, 1, 2, 5, 7, 10, 11, 16, 21, 26, 29, 35, 37, 40, 43, 51, 56, 65, 70, 78, 83, 87, 89, 98, 103, 108, 115, 124, 129, 137, 139, 150, 159, 167, 175, 188, 194, 201, 207, 218, 223, 232, 235, 242, 250, 255, 258, 271, 278, 288, 296, 305, 310
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033096, A033098, A033100, A033102, A033104, A033106, A033108, A033110, A033112.

Programs

  • Mathematica
    f[n_] := Count[ Flatten@ Table[ IntegerDigits[k, b], {k, n}, {b, 2, n + 1}], 0]; Array[f, 53] (* Robert G. Wilson v, Nov 14 2012 *)

A033095 Number of 1's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

1, 1, 3, 4, 6, 6, 9, 6, 10, 10, 12, 11, 16, 13, 15, 14, 16, 13, 18, 15, 21, 20, 21, 16, 24, 20, 23, 23, 26, 25, 32, 22, 26, 25, 25, 28, 34, 28, 32, 30, 35, 30, 37, 31, 35, 36, 35, 31, 41, 34, 37, 36, 39, 35, 43, 38, 44, 41, 42, 38, 49, 40, 43
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A053735, A053737, A062756, A077267.
Cf. A033093, A033096, A033097, A033099, A033101, A033103, A033105, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 1]; Array[f, 63] (* Robert G. Wilson v, Nov 14 2012 *)

Formula

G.f.: x+(Sum_{b>=2} (Sum_{k>=0} x^(b^k)/(Sum_{0<=iFranklin T. Adams-Watters, Nov 03 2005

A033097 Number of 2's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

0, 1, 0, 0, 1, 2, 2, 4, 2, 4, 4, 4, 3, 7, 4, 6, 7, 7, 5, 9, 5, 9, 8, 9, 8, 14, 7, 7, 8, 9, 6, 13, 8, 12, 12, 10, 11, 16, 9, 11, 12, 16, 11, 16, 10, 14, 15, 12, 11, 20, 14, 17, 16, 15, 12, 19, 15, 19, 16, 16, 15, 25, 15, 17, 19, 19, 17, 21, 16, 19, 18
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033098, A033099, A033101, A033103, A033105, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 2]; Array[f, 70] (* Robert G. Wilson v, Nov 14 2012 *)

A033099 Number of 3's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033097, A033100, A033101, A033103, A033105, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 3]; Array[f, 80] (* Robert G. Wilson v, Nov 14 2012 *)

A033101 Number of 4's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033097, A033099, A033102, A033103, A033105, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 4]; Array[f, 88] (* Robert G. Wilson v, Nov 14 2012 *)

A033103 Number of 5's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033097, A033099, A033101, A033104, A033105, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 5]; Array[f, 90] (* Robert G. Wilson v, Nov 14 2012 *)

A033105 Number of 6's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 2, 5, 2, 3, 3, 5, 2, 6, 2, 4, 4, 3, 2, 7, 4, 4, 3, 4, 2, 6, 4, 7, 3, 3, 2, 8, 3, 4, 6, 5, 3, 6, 3, 5, 4, 7, 2, 9, 3, 4, 5, 5, 5, 6, 3, 8, 5, 4, 3, 10
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033097, A033099, A033101, A033103, A033106, A033107, A033109, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 6]; Array[f, 90] (* Robert G. Wilson v, Nov 14 2012 *)

A033109 Number of 8's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 4, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 6, 1, 2, 3, 4, 3, 5, 2, 4, 3, 5, 2, 8, 2, 3, 4, 4, 3, 5, 2, 7, 5, 3
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A033093, A033095, A033097, A033099, A033101, A033103, A033105, A033107, A033110, A033111.

Programs

  • Mathematica
    f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 8]; Array[f, 90] (* Robert G. Wilson v, Nov 14 2012 *)
Showing 1-10 of 14 results. Next

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