A329923 Beatty sequence for (2+sqrt(34))/5.

1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 57, 59, 61, 62, 64, 65, 67, 68, 70, 72, 73, 75, 76, 78, 79, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 97, 98, 100, 101

Offset

1,2

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..65.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*r), where r = (2+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, A329924 (complement).

Sequence in context: A093610 A206912 A330113 * A187342 A330143 A140758

Adjacent sequences: A329920 A329921 A329922 * A329924 A329925 A329926

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved