A329833 Beatty sequence for (5+sqrt(73))/8.

1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 94, 96, 98, 99, 101, 103, 104, 106, 108

Offset

1,2

Comments

Let r = (5+sqrt(73))/8. Then (floor(n*r)) and (floor(n*r + 3r/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..64.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*r), where r = (5+sqrt(73))/8.

Mathematica

t = 3/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329833 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329834 *)

Crossrefs

Cf. A329825, A329834 (complement).

Sequence in context: A329993 A064994 A138235 * A059541 A189682 A003152

Adjacent sequences: A329830 A329831 A329832 * A329834 A329835 A329836

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2019

Status

approved