A253301 Complement of the Beatty sequence for sqrt(Pi*phi), where phi is the golden ratio.

1, 3, 5, 7, 8, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 53, 55, 57, 59, 61, 62, 64, 66, 68, 70, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 98, 100, 102, 104, 106, 107, 109, 111, 113, 115

Offset: 1

Author

Colin Barker, Dec 30 2014

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Beatty Sequence

Crossrefs

Cf. A252169, A001622 (golden ratio, phi), A094886 (Pi*phi).

Programs

Mathematica

Table[Floor[n*Sqrt[Pi*GoldenRatio]/(Sqrt[Pi*GoldenRatio] - 1)], {n, 1, 100}] (* G. C. Greubel, Jan 09 2017 *)

PARI

phi = (sqrt(5)+1)/2; vector(100, n, floor(n*sqrt(Pi*phi) / (sqrt(Pi*phi)-1)))

Formula

a(n) = floor(n*sqrt(Pi*phi)/(sqrt(Pi*phi)-1)), where phi is the golden ratio.