A329926 Beatty sequence for (9+sqrt(41))/5.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 154, 157, 160, 163, 166, 169, 172, 175, 178, 181

Offset: 1

Author

Clark Kimberling, Jan 02 2020

Keywords

• nonn
• easy

Comments

Let r = (1+sqrt(41))/5. Then (floor(n*r)) and (floor(n*r + 8r/5)) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.

Links

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

Crossrefs

Cf. A329825, A329925 (complement).

Programs

Mathematica

t = 8/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329925 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329926 *)

Formula

a(n) = floor(n*s), where s = (9+sqrt(41))/5.

Extensions

Definition corrected by Georg Fischer, Jul 08 2021