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A078796
a(n) = 2*ceiling(n*tau) - ceiling(n*sqrt(5)) where tau=(1+sqrt(5))/2 is the Golden ratio.
1
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
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Dec 05 2002
STATUS
approved