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

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Beatty Sequence

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A059565 A329999 A187841 * A379979 A003144 A247357

Adjacent sequences: A253298 A253299 A253300 * A253302 A253303 A253304

Keyword

nonn,changed

Author

Colin Barker, Dec 30 2014

Status

approved