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

1,1

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

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

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

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 *)

Crossrefs

Cf. A329825, A329925 (complement).

Sequence in context: A135943 A194416 A036686 * A194423 A059563 A292641

Adjacent sequences: A329923 A329924 A329925 * A329927 A329928 A329929

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Extensions

Definition corrected by Georg Fischer, Jul 08 2021

Status

approved