A164086 Beatty sequence for 4*Pi/3 = 4.1887902... .

4, 8, 12, 16, 20, 25, 29, 33, 37, 41, 46, 50, 54, 58, 62, 67, 71, 75, 79, 83, 87, 92, 96, 100, 104, 108, 113, 117, 121, 125, 129, 134, 138, 142, 146, 150, 154, 159, 163, 167, 171, 175, 180, 184, 188, 192, 196, 201, 205, 209, 213, 217, 222, 226, 230, 234, 238, 242

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2009

Keywords

• nonn

Comments

a(n) = A109238(n) for n <= 20;

complement of A164087;

a(n) = A164088(A164087(n)) and A164088(a(n)) = A164087(n);

a(A000578(n)) = A066645(n).

Examples

			a(3^3) = a(27) = 113 = (integer part of volume of sphere with radius=3) = A066645(3).
		

Links

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

Crossrefs

Cf. A022844, A019699.

Programs

Mathematica

With[{c=4 \[Pi]/3},Floor[c #]&/@Range[70]]  (* Harvey P. Dale, Mar 19 2011 *)

Maxima

fprec:100$
A164086:4*%pi/3$
ev(bfloat(A164086)); /* Martin Ettl, Nov 03 2012 */

Formula

a(n) = floor(4*n*Pi/3).