A329831 Beatty sequence for (7+sqrt(65))/8.

1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 99, 101, 103, 105, 107, 109, 111, 112, 114, 116, 118

Offset

1,2

Comments

Let r = (7+sqrt(65))/8. Then (floor(n*r)) and (floor(n*r + r/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..63.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*r), where r = (7+sqrt(65))/8.

Mathematica

t = 1/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329831 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329832 *)

Crossrefs

Cf. A329825, A329832 (complement).

Sequence in context: A134322 A186328 A063460 * A329938 A247429 A187232

Adjacent sequences: A329828 A329829 A329830 * A329832 A329833 A329834

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2019

Status

approved