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.

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

A140758 a(n) = floor(n*Pi/2).

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 76, 78, 80, 81, 83, 84, 86, 87, 89, 91, 92, 94, 95, 97, 98, 100, 102, 103, 105
Offset: 0

Views

Author

Reinhard Zumkeller, May 27 2008

Keywords

Comments

Beatty sequence for Pi/2; complement of A108589; not the same as A093610: a(23)=36 <> A093610(23)=35.

Examples

			For n = 5, 5*(Pi/2) approximately equals 7.854, and floor(7.854) = 7.

Links

Crossrefs

Cf. A022844, A038130, A108590.

Programs

  • Magma
    R:= RealField(40); [Floor(n*Pi(R)/2): n in [0..80]]; // G. C. Greubel, Oct 21 2023
  • Mathematica
    Floor[Pi*Range[0,80]/2] (* G. C. Greubel, Oct 21 2023 *)
  • Python
    import math
x=0
while x < 36001:
    y = math.radians(x)
    z = math.trunc(y)
    print(z, end=", ")
    x += 90
# Mick Purcell (mickpurcell(AT)gmail.com), Oct 05 2009
  • SageMath
    [floor(n*pi/2) for n in range(81)] # G. C. Greubel, Oct 21 2023

Extensions

0 added by Mick Purcell (mickpurcell(AT)gmail.com), Oct 05 2009

A108590 Self-inverse integer permutation induced by Beatty sequences for Pi/2 and Pi/(Pi-2).

Original entry on oeis.org

2, 1, 5, 8, 3, 11, 13, 4, 16, 19, 6, 22, 7, 24, 27, 9, 30, 33, 10, 35, 38, 12, 41, 14, 44, 46, 15, 49, 52, 17, 55, 57, 18, 60, 20, 63, 66, 21, 68, 71, 23, 74, 77, 25, 79, 26, 82, 85, 28, 88, 90, 29, 93, 96, 31, 99, 32, 101, 104, 34, 107, 110, 36, 112, 115, 37, 118, 39, 121
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108591, A108592.

Formula

a(A140758(n))=A108589(n) and a(A108589(n))=A140758(n).

A292988 Beatty sequence of the real root of 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1; complement of A292987.

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, 170, 173, 176, 179
Offset: 1

Views

Author

Iain Fox, Dec 08 2017

Keywords

Comments

First differs from A187341 at n = 21.
First differs from A108589 at n = 65.

Examples

			a(2) = floor(2 * 2.7539...) = floor(5.5078...) = 5.

Links

Crossrefs

Cf. A187341, A108589.
Complement: A292987.

Programs

  • Mathematica
    r = N[ Root[2#^5 - 9#^4 + 13#^3 - 11#^2 + 5# - 1 &, 1], 64]; Array[ Floor[r #] &, 70] (* Robert G. Wilson v, Dec 10 2017 *)
  • PARI
    a(n) = floor(n*solve(x=2, 3, 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1))

Formula

a(n) = floor(n * r), where r = 2.75393267425618214080...
Showing 1-4 of 4 results.

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