A329843 Beatty sequence for (1+sqrt(61))/6.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 93, 95, 96

Offset: 1

Author

Clark Kimberling, Jan 02 2020

Keywords

• nonn
• easy

Comments

Let r = (1+sqrt(61))/6. Then (floor(n*r)) and (floor(n*r + 5r/3)) 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, A329844 (complement).

Programs

Mathematica

t = 5/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329843 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329844 *)

Formula

a(n) = floor(n*r), where r = (1+sqrt(61))/6.