A329838 Beatty sequence for (6+sqrt(26))/5.

2, 4, 6, 8, 11, 13, 15, 17, 19, 22, 24, 26, 28, 31, 33, 35, 37, 39, 42, 44, 46, 48, 51, 53, 55, 57, 59, 62, 64, 66, 68, 71, 73, 75, 77, 79, 82, 84, 86, 88, 91, 93, 95, 97, 99, 102, 104, 106, 108, 110, 113, 115, 117, 119, 122, 124, 126, 128, 130, 133, 135

Offset: 1

Author

Clark Kimberling, Dec 31 2019

Keywords

• nonn
• easy

Comments

Let r = (4+sqrt(26))/5. Then (floor(n*r)) and (floor(n*r + 2r/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

• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A329825, A329837 (complement).

Programs

Mathematica

t = 2/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329837 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329838 *)

Formula

a(n) = floor(n*s), where s = (6+sqrt(26))/5.