A329925 Beatty sequence for (1+sqrt(41))/5.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97

Offset: 1

Author

Clark Kimberling, Jan 02 2020

Keywords

• nonn
• easy

Comments

Let r = (1+sqrt(41))/5. Then (floor(n*r)) and (floor(n*r + 8r/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, A329926 (complement).

Programs

Mathematica

t = 8/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329925 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329926 *)

Formula

a(n) = floor(n*r), where r = (1+sqrt(41))/5.