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

Author

Felice Russo

Keywords

• nonn

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

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

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