A329836 Beatty sequence for (11+sqrt(101))/10.

2, 4, 6, 8, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 42, 44, 46, 48, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 82, 84, 86, 88, 90, 92, 94, 96, 98, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 122, 124, 126, 128, 130

Offset: 1

Author

Clark Kimberling, Dec 31 2019

Keywords

• nonn
• easy

Comments

Let r = (9+sqrt(101))/10. 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, A329835 (complement).

Programs

Mathematica

t = 1/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329835 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329836 *)

Formula

a(n) = floor(n*s), where s = (11+sqrt(101))/10.