A195121 a(n) = 2*n - floor(n/r), where r = (1 + sqrt(5))/2 (the golden ratio).

0, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 88, 89, 90, 92, 93, 94

Offset: 0

Author

Clark Kimberling, Sep 09 2011

Keywords

• nonn

Comments

Apparently, the nonzero terms are the numbers whose maximal Lucas representation (A130311) ends with 1. - Amiram Eldar, Jan 21 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001622, A130311.

Programs

Magma

[3*n-Floor(n*(1+Sqrt(5))/2): n in [0..70]]; // Vincenzo Librandi, Sep 12 2011

Mathematica

Table[2n-Floor[n/GoldenRatio],{n,0,70}] (* Harvey P. Dale, Feb 11 2018 *)

Formula

a(n) = 3*n - floor(n*r), where r = (1 + sqrt(5))/2.