A182761 Beatty sequence for (7 - sqrt(5))/2.

2, 4, 7, 9, 11, 14, 16, 19, 21, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 54, 57, 59, 61, 64, 66, 69, 71, 73, 76, 78, 80, 83, 85, 88, 90, 92, 95, 97, 100, 102, 104, 107, 109, 111, 114, 116, 119, 121, 123, 126, 128, 131, 133

Offset: 1

Author

Clark Kimberling, Nov 28 2010

Keywords

• nonn

Comments

See the first comment at A182760; its complement, A182761, gives the positions of the numbers k*sqrt(5) when these numbers and the numbers j*u, where u = golden ratio, are jointly ranked.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A182760.

Programs

Magma

[Floor(n*(7-5^(1/2))/2): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011

Mathematica

Table[Floor[n*(7-Sqrt[5])/2], {n,1,80}] (* G. C. Greubel, Jul 08 2018 *)

PARI

for(n=1,80, print1(floor(n*(7-sqrt(5))/2), ", ")) \\ G. C. Greubel, Jul 08 2018

Formula

a(n) = floor(n*(7 - sqrt(5))/2).

Extensions

Typo in formula corrected by Vincenzo Librandi, Oct 25 2011