A329848 Beatty sequence for (13+sqrt(89))/8.

2, 5, 8, 11, 14, 16, 19, 22, 25, 28, 30, 33, 36, 39, 42, 44, 47, 50, 53, 56, 58, 61, 64, 67, 70, 72, 75, 78, 81, 84, 86, 89, 92, 95, 98, 100, 103, 106, 109, 112, 114, 117, 120, 123, 126, 128, 131, 134, 137, 140, 143, 145, 148, 151, 154, 157, 159, 162, 165

Offset: 1

Author

Clark Kimberling, Jan 02 2020

Keywords

• nonn
• easy

Comments

Let r = (3+sqrt(89))/8. Then (floor(n*r)) and (floor(n*r + 5r/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, A329847 (complement).

Programs

Mathematica

t = 5/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329847 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329848 *)

Formula

a(n) = floor(n*s), where s = (13+sqrt(89))/8.