A329834 Beatty sequence for (11+sqrt(73))/8.

2, 4, 7, 9, 12, 14, 17, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 65, 68, 70, 73, 75, 78, 80, 83, 85, 87, 90, 92, 95, 97, 100, 102, 105, 107, 109, 112, 114, 117, 119, 122, 124, 127, 129, 131, 134, 136, 139, 141, 144, 146

Offset: 1

Author

Clark Kimberling, Dec 31 2019

Keywords

• nonn
• easy

Comments

Let r = (5+sqrt(73))/8. Then (floor(n*r)) and (floor(n*r + 3r/4)) 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, A329833 (complement).

Programs

Mathematica

t = 3/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329833 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329834 *)

Formula

a(n) = floor(n*s), where s = (11+sqrt(73))/8.