A329924 Beatty sequence for (8+sqrt(34))/5.

2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 47, 49, 52, 55, 58, 60, 63, 66, 69, 71, 74, 77, 80, 82, 85, 88, 91, 94, 96, 99, 102, 105, 107, 110, 113, 116, 118, 121, 124, 127, 130, 132, 135, 138, 141, 143, 146, 149, 152, 154, 157, 160, 163

Offset

1,1

Comments

Let r = (2+sqrt(34))/5. Then (floor(n*r)) and (floor(n*r + 6r/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

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 = (8+sqrt(34))/5.

Mathematica

t = 6/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329923 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329924 *)

Crossrefs

Cf. A329825, A329923 (complement).

Sequence in context: A292988 A330144 A187341 * A330112 A206911 A093609

Adjacent sequences: A329921 A329922 A329923 * A329925 A329926 A329927

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved