A195170 a(n) = 4*n - floor(n*r), where r=(1+sqrt(5))/2 (the golden ratio).

0, 3, 5, 8, 10, 12, 15, 17, 20, 22, 24, 27, 29, 31, 34, 36, 39, 41, 43, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 70, 72, 74, 77, 79, 81, 84, 86, 89, 91, 93, 96, 98, 101, 103, 105, 108, 110, 112, 115, 117, 120, 122, 124, 127, 129, 132, 134, 136, 139, 141, 143

Offset

0,2

Links

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

Formula

a(n) = n + A195121(n) = 4*n- A000201(n). - R. J. Mathar, Sep 11 2011

Mathematica

With[{c = GoldenRatio}, Table[4*n - Floor[c*n], {n, 0, 50}]] (* G. C. Greubel, Oct 31 2017 *)

Prog

(Magma) [4*n-Floor(n*(1+Sqrt(5))/2): n in [0..70]]; // Vincenzo Librandi, Sep 11 2011
(PARI) for(n=0, 50, print1(4*n - floor(n*(1+sqrt(5))/2), ", ")) \\ G. C. Greubel, Oct 31 2017
(Python)
from math import isqrt
def A195170(n): return (n<<2)-(n+isqrt(5*n**2)>>1) # Chai Wah Wu, Aug 10 2022

Crossrefs

Sequence in context: A047391 A184655 A090846 * A079527 A287236 A305378

Adjacent sequences: A195167 A195168 A195169 * A195171 A195172 A195173

Keyword

nonn

Author

Clark Kimberling, Sep 10 2011

Status

approved