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.

A038130 Beatty sequence for 2*Pi.

Original entry on oeis.org

0, 6, 12, 18, 25, 31, 37, 43, 50, 56, 62, 69, 75, 81, 87, 94, 100, 106, 113, 119, 125, 131, 138, 144, 150, 157, 163, 169, 175, 182, 188, 194, 201, 207, 213, 219, 226, 232, 238, 245, 251, 257, 263, 270, 276, 282, 289, 295, 301, 307, 314, 320, 326, 333, 339, 345
Offset: 0

Views

Author

Felice Russo

Keywords

Comments

a(n) = floor[circumference of a circle of radius n]. - Mohammad K. Azarian, Feb 29 2008
This sequence consists of the nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) >= 0; thus this sequence and A246388 partition A022844 (the Beatty sequence for Pi). - Clark Kimberling, Aug 24 2014

Links

Crossrefs

Complement of A108586.
For ceiling (2*Pi*n) see A004082.
Cf. A022844, A140758, A108592, A246388.

Programs

  • Mathematica
    Table[Floor[2 n*Pi], {n, 0, 100}] (* or *)
Select[Range[0, 628], Sin[#] <= 0 && Sin[# + 1] >= 0 &] (* Clark Kimberling, Aug 24 2014 *)

Formula

a(n) = floor(2*Pi*n).
a(n) = A004082(n+1) - 1. - John W. Nicholson, Mar 20 2025

Extensions

More terms from Mohammad K. Azarian, Feb 29 2008

A054386 Beatty sequence for Pi/(Pi-1); complement of A022844.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

Differs from A127450 at term n=122, where A054386(122)=178, A127450(122)=179. - Martin Fuller, May 10 2007

Links

Crossrefs

Cf. A022844, A108586, A108589, A108591.

Programs

  • Magma
    R:=RealField(30); [Floor(n*Pi(R)/(Pi(R)-1)): n in [1..80]]; // G. C. Greubel, Oct 22 2023
  • Mathematica
    Floor[Pi*Range[80]/(Pi-1)] (* G. C. Greubel, Oct 22 2023 *)
  • SageMath
    [floor(n*pi/(pi-1)) for n in range(1,81)] # G. C. Greubel, Oct 22 2023

A108120 Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 85
Offset: 1

Views

Author

Zak Seidov, Jun 04 2005

Keywords

Comments

Complement of A108587; not the same as A108586: a(37)=43 <> A108586(37)=44. - Reinhard Zumkeller, Jun 11 2005

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253.
Cf. A108593.

Programs

  • Mathematica
    a[n_]:=Floor[n*1/Sin[1]];Table[a[n], {n, 90}]

Formula

a(n) = floor(n*1/sin(1))

A108589 a(n) = floor(n*Pi/(Pi-2)).

Original entry on oeis.org

2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 46, 49, 52, 55, 57, 60, 63, 66, 68, 71, 74, 77, 79, 82, 85, 88, 90, 93, 96, 99, 101, 104, 107, 110, 112, 115, 118, 121, 123, 126, 129, 132, 134, 137, 140, 143, 145, 148, 151, 154, 156, 159, 162, 165, 167
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Comments

Beatty sequence for Pi/(Pi-2); complement of A140758.

Links

Crossrefs

Cf. A054386, A108586, A108590, A140758.

Programs

  • Magma
    R:= RealField(40); [Floor(n*Pi(R)/(Pi(R)-2)): n in [1..60]]; // G. C. Greubel, Oct 21 2023
  • Maple
    A108589:=n->floor(n*Pi/(Pi-2)); seq(A108589(n), n=1..50); # Wesley Ivan Hurt, Apr 19 2014
  • Mathematica
    With[{c=Pi/(Pi-2)},Floor[c*Range[70]]] (* Harvey P. Dale, Apr 19 2014 *)
  • SageMath
    [floor(n*pi/(pi-2)) for n in range(1,61)] # G. C. Greubel, Oct 21 2023

A108592 Self-inverse integer permutation induced by Beatty sequences for 2*Pi and 2*Pi/(2*Pi-1).

Original entry on oeis.org

6, 12, 18, 25, 31, 1, 37, 43, 50, 56, 62, 2, 69, 75, 81, 87, 94, 3, 100, 106, 113, 119, 125, 131, 4, 138, 144, 150, 157, 163, 5, 169, 175, 182, 188, 194, 7, 201, 207, 213, 219, 226, 8, 232, 238, 245, 251, 257, 263, 9, 270, 276, 282, 289, 295, 10, 301, 307, 314, 320, 326, 11, 333, 339, 345, 351, 358, 364, 13, 370
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108590, A108591, A108593.

Programs

  • PARI
    a30(n) = floor(n*2*Pi);
a86(n) = floor(2*n*Pi/(2*Pi-1));
lista(nn) = {my(vb = vector(nn, n, a30(n))); my(vc = vector(nn, n, a86(n))); my(va = vector(nn)); for (n=1, nn, if (vb[n] <= nn, va[vb[n]] = vc[n]); if (vc[n] <= nn, va[vc[n]] = vb[n]);); va;} \\ Michel Marcus, May 25 2022

Formula

a(A038130(n))=A108586(n) and a(A108586(n))=A038130(n).

Extensions

Four terms corrected by Georg Fischer and Michel Marcus, May 25 2022
Showing 1-5 of 5 results.

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