A108590 -id:A108590 - cp's OEIS frontend

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

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

Reinhard Zumkeller, May 27 2008

nonn

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

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

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences related to Beatty sequences

Cf. A022844, A038130, A108590.

R:= RealField(40); [Floor(n*Pi(R)/2): n in [0..80]]; // G. C. Greubel, Oct 21 2023

Floor[Pi*Range[0,80]/2] (* G. C. Greubel, Oct 21 2023 *)

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

[floor(n*pi/2) for n in range(81)] # G. C. Greubel, Oct 21 2023

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

A108591 Self-inverse integer permutation induced by Beatty sequences for Pi and Pi/(Pi-1).

Original entry on oeis.org

3, 6, 1, 9, 12, 2, 15, 18, 4, 21, 25, 5, 28, 31, 7, 34, 37, 8, 40, 43, 10, 47, 50, 53, 11, 56, 59, 13, 62, 65, 14, 69, 72, 16, 75, 78, 17, 81, 84, 19, 87, 91, 20, 94, 97, 100, 22, 103, 106, 23, 109, 113, 24, 116, 119, 26, 122, 125, 27, 128, 131, 29, 135, 138, 30, 141, 144

Offset: 1

Reinhard Zumkeller, Jun 11 2005

Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to Beatty sequences

Cf. A108590, A108592, A108599.

a(A022844(n))=A054386(n) and a(A054386(n))=A022844(n).

a(53)/a(54) joined by Georg Fischer, May 24 2022

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

Reinhard Zumkeller, Jun 11 2005

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

Vincenzo Librandi, Table of n, a(n) for n = 1..7000
Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences related to Beatty sequences

Cf. A054386, A108586, A108590, A140758.

R:= RealField(40); [Floor(n*Pi(R)/(Pi(R)-2)): n in [1..60]]; // G. C. Greubel, Oct 21 2023

A108589:=n->floor(n*Pi/(Pi-2)); seq(A108589(n), n=1..50); # Wesley Ivan Hurt, Apr 19 2014

With[{c=Pi/(Pi-2)},Floor[c*Range[70]]] (* Harvey P. Dale, Apr 19 2014 *)

[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 2Pi and 2Pi/(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

Reinhard Zumkeller, Jun 11 2005

Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to Beatty sequences

Cf. A108590, A108591, A108593.

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

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

Four terms corrected by Georg Fischer and Michel Marcus, May 25 2022

cp's OEIS Frontend

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

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A108591 Self-inverse integer permutation induced by Beatty sequences for Pi and Pi/(Pi-1).

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

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

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