A329842 Beatty sequence for (13+sqrt(109))/10.

2, 4, 7, 9, 11, 14, 16, 18, 21, 23, 25, 28, 30, 32, 35, 37, 39, 42, 44, 46, 49, 51, 53, 56, 58, 60, 63, 65, 67, 70, 72, 75, 77, 79, 82, 84, 86, 89, 91, 93, 96, 98, 100, 103, 105, 107, 110, 112, 114, 117, 119, 121, 124, 126, 128, 131, 133, 135, 138, 140, 142

Offset

1,1

Comments

Let r = (13+sqrt(109))/10. Then (floor(n*r)) and (floor(n*r + 3r/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..61.

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(109))/10.

Mathematica

t = 3/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329841 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329842 *)

Crossrefs

Cf. A329825, A329841 (complement).

Sequence in context: A187686 A024812 A047349 * A054406 A292647 A356085

Adjacent sequences: A329839 A329840 A329841 * A329843 A329844 A329845

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2019

Status

approved