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 1-4 of 4 results.

A240977 Beatty sequence for cube root of Pi: a(n) = floor(n*Pi^(1/3)).

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 84
Offset: 0

Views

Author

Sarah Nathanson, Sep 30 2014

Keywords

Comments

Beatty complement of A248524. - M. F. Hasler, Oct 07 2014

Links

Crossrefs

Cf. A092039 (Pi^(1/3)), A022844 (similar for Pi), A037086 (similar for sqrt(Pi)), A248524.

Programs

  • Java
    static int a(int n) {return (int) (n*Math.pow(Math.PI,(1.0/3)));}
  • Mathematica
    Table[Floor[n*(Pi^(1/3))], {n, 0, 50}] (* G. C. Greubel, Feb 14 2017 *)
  • PARI
    a(n)=n\Pi^(-1/3) \\ M. F. Hasler, Oct 07 2014

Formula

a(n) = floor(n*(Pi^1/3)).

Extensions

a(0)=0 prepended by Eric M. Schmidt, Oct 06 2014
Name edited by M. F. Hasler, Oct 07 2014

A248524 Beatty sequence for 1/(1-Pi^(-1/3)).

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 22, 25, 28, 31, 34, 37, 40, 44, 47, 50, 53, 56, 59, 63, 66, 69, 72, 75, 78, 81, 85, 88, 91, 94, 97, 100, 104, 107, 110, 113, 116, 119, 122, 126, 129, 132, 135, 138, 141, 145, 148, 151, 154, 157, 160, 163, 167, 170, 173, 176, 179, 182
Offset: 1

Views

Author

M. F. Hasler, Oct 07 2014

Keywords

Comments

Beatty complement of A240977.

Links

Crossrefs

Cf. A092039 (Pi^(1/3)), A093204 (Pi^(-1/3)), A022844 (Beatty seq. for Pi), A037086 (Beatty seq. for sqrt(Pi)).

Programs

  • Mathematica
    Table[Floor[n/(1 - Pi^(-1/3))], {n, 1, 50}] (* G. C. Greubel, Apr 06 2017 *)
  • PARI
    a(n)=n\(1-Pi^(-1/3))

Formula

a(n) = floor(n/(1-Pi^(-1/3))).

A277050 a(n) = floor(2*n/sqrt(Pi)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75
Offset: 0

Views

Author

Paulo Romero Zanconato Pinto, Sep 26 2016

Keywords

Links

Crossrefs

Cf. A037086, A190732, A277052 (complement).

Programs

  • Maple
    A277050:=n->floor(2*n/sqrt(Pi)): seq(A277050(n), n=0..100); # Wesley Ivan Hurt, Sep 26 2016
  • Mathematica
    Table[Floor[2 * n/Sqrt[Pi]], {n, 100}]
  • PARI
    a(n) = floor(2*n/sqrt(Pi));

Formula

a(n) = floor(2*n/sqrt(Pi)).

A277052 a(n) = n+floor(n/(2/sqrt(Pi)-1)).

Original entry on oeis.org

8, 17, 26, 35, 43, 52, 61, 70, 79, 87, 96, 105, 114, 123, 131, 140, 149, 158, 166, 175, 184, 193, 202, 210, 219, 228, 237, 246, 254, 263, 272, 281, 290, 298, 307, 316, 325, 333, 342, 351, 360, 369, 377, 386, 395, 404, 413, 421, 430, 439, 448, 457, 465, 474
Offset: 1

Views

Author

Paulo Romero Zanconato Pinto, Sep 26 2016

Keywords

Links

Crossrefs

Complement of A277050.
Cf. A190732, A037086.

Programs

  • Maple
    A277052:=n->n+floor(n/(2/sqrt(Pi)-1)): seq(A277052(n), n=1..100); # Wesley Ivan Hurt, Sep 26 2016
  • Mathematica
    f[n_] := n + Floor[n/(2/Sqrt[Pi]-1)]; Array[f, 100, 1]
  • PARI
    a(n) = n + floor(n/(2/sqrt(Pi)-1));

Formula

a(n) = n + floor(n/(2/sqrt(Pi) - 1)).
Showing 1-4 of 4 results.

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