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

1,2

Links

Table of n, a(n) for n=1..72.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001950, A005652, A078588.

Sequence in context: A134636 A088564 A161560 * A201929 A079789 A131209

Adjacent sequences: A078793 A078794 A078795 * A078797 A078798 A078799

Keyword

nonn

Author

Benoit Cloitre, Dec 05 2002

Status

approved