A078796 a(n) = 2*ceiling(n*tau) - ceiling(n*sqrt(5)) where tau=(1+sqrt(5))/2 is the Golden ratio.

1, 3, 3, 5, 6, 6, 8, 8, 9, 11, 11, 13, 14, 14, 16, 16, 17, 19, 19, 21, 21, 22, 24, 24, 26, 27, 27, 29, 29, 30, 32, 32, 34, 35, 35, 37, 37, 39, 40, 40, 42, 42, 43, 45, 45, 47, 48, 48, 50, 50, 51, 53, 53, 55, 55, 56, 58, 58, 60, 61, 61, 63, 63, 64, 66, 66, 68, 69, 69, 71, 71, 73

Offset: 1

Author

Benoit Cloitre, Dec 05 2002

Keywords

• nonn

Crossrefs

Cf. A001950, A005652, A078588.

Programs

Mathematica

Table[2*Ceiling[n*GoldenRatio]-Ceiling[n*Sqrt[5]],{n,80}] (* Harvey P. Dale, Dec 20 2015 *)

PARI

a(n)=2*ceil(n*(1+sqrt(5))/2)-ceil(n*sqrt(5))

Python

from math import isqrt
def A078796(n): return (n+(m:=isqrt(5*n**2))&-2)-m+1 # Chai Wah Wu, Aug 17 2022

Formula

a(A005652(n)) = A005652(n); a(A001950(n)) = A001950(n) + 1.