A078796 - OEIS

%I #14 Aug 17 2022 22:20:29

%S 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,

%T 27,29,29,30,32,32,34,35,35,37,37,39,40,40,42,42,43,45,45,47,48,48,50,

%U 50,51,53,53,55,55,56,58,58,60,61,61,63,63,64,66,66,68,69,69,71,71,73

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

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

%t Table[2*Ceiling[n*GoldenRatio]-Ceiling[n*Sqrt[5]],{n,80}] (* _Harvey P. Dale_, Dec 20 2015 *)

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

%o (Python)

%o from math import isqrt

%o def A078796(n): return (n+(m:=isqrt(5*n**2))&-2)-m+1 # _Chai Wah Wu_, Aug 17 2022

%Y Cf. A001950, A005652, A078588.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Dec 05 2002