A004082 -id:A004082 - cp's OEIS frontend

A038130 Beatty sequence for 2*Pi.

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

Felice Russo

nonn

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

Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences.

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

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

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

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

More terms from Mohammad K. Azarian, Feb 29 2008

A277690 Smallest possible number of sides of a regular polygon with unit sides and circumradius at least n.

Original entry on oeis.org

3, 6, 13, 19, 26, 32, 38, 44, 51, 57, 63, 70, 76, 82, 88, 95, 101, 107, 114, 120, 126, 132, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 308, 315

Offset: 0

John D. Dixon, Oct 26 2016

nonn

The average difference between terms in the sequence approaches 2*Pi.

Limit_{n -> oo} d/dn (Pi / arcsin(1/2n)) = 2*Pi.

			a(0) = 3, since this is the smallest number of sides a regular polygon may have;
a(1) = ceiling( Pi / arcsin(1/2) ) = ceiling( Pi/(Pi/6) ) = 6;
a(2) = ceiling( Pi / arcsin(1/4) ) = ceiling( Pi/(0.2526...) ) = 13;
...

See A004082 for another version.

As a function, this is the inverse of A067099.

Table[If[n == 0, 3, Ceiling[Pi/ArcSin[1/(2 n)]]], {n, 0, 50}] (* Michael De Vlieger, Oct 28 2016 *) (* corrected on Aug 28 2023 by John D. Dixon *)

a(n) = if (n==0, 3, ceil(Pi/asin(1/(2*n)))); \\ Michel Marcus, Oct 28 2016; corrected Jun 13 2022 \\ corrected again on Aug 28 2023 by John D. Dixon

a(n) = ceiling( Pi / arcsin(1/(2*n)) ).

First term and definition corrected by John D. Dixon, Aug 28 2023

cp's OEIS Frontend

A038130 Beatty sequence for 2*Pi.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions