A329844 Beatty sequence for (11+sqrt(61))/6.

3, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 40, 43, 47, 50, 53, 56, 59, 62, 65, 68, 72, 75, 78, 81, 84, 87, 90, 94, 97, 100, 103, 106, 109, 112, 115, 119, 122, 125, 128, 131, 134, 137, 141, 144, 147, 150, 153, 156, 159, 163, 166, 169, 172, 175, 178, 181

Offset

1,1

Comments

Let r = (1+sqrt(61))/6. Then (floor(n*r)) and (floor(n*r + 5r/3)) 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..58.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*s), where s = (11+sqrt(61))/6.

Mathematica

t = 5/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329843 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329844 *)

Crossrefs

Cf. A329825, A329843 (complement).

Sequence in context: A117124 A323422 A071073 * A127451 A022844 A260702

Adjacent sequences: A329841 A329842 A329843 * A329845 A329846 A329847

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved