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

1,1

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

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

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

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 *)

Crossrefs

Cf. A329825, A329847 (complement).

Sequence in context: A257771 A276881 A282457 * A059560 A022842 A356057

Adjacent sequences: A329845 A329846 A329847 * A329849 A329850 A329851

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved