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