A048581 - OEIS

%I #17 Jul 04 2018 06:26:29

%S 47,53,829,79,857,1901,5273,97,1787,5563,4519,4057,19139,743,25681,

%T 229,3687,18647,8329,3853,51067,28069,20483,335,72791,4379,85093,

%U 22901,6557,52673,112577,2501,127759,13571,15989,38083,161003,28319,35813

%N Numerators of b(n) = (1/16^n)*(4/(8*n+1) - 2/(8*n+4) - 1/(8*n+5) - 1/(8*n+6)).

%C Sum_{k>=0} b(k) = Pi was the first BBP formula for Pi (Bayley-Borwein-Plouffe in 1995). Allows one to extract any specified binary digit of Pi.

%H G. C. Greubel, <a href="/A048581/b048581.txt">Table of n, a(n) for n = 0..1000</a>

%H B. Gourevitch, <a href="http://www.pi314.net">L'univers de Pi</a>

%F Sum_{k>=0} b(k) = Pi.

%F a(n) = numerator((1/16)^n*sum(i=1,4,((-1)^(ceiling(4/(2*i))))*(floor(4/i))/(8*n+i+floor(sqrt(i-1))*(floor(sqrt(i-1))+1)))). - _Alexander R. Povolotsky_, Aug 31 2009

%t Numerator[Table[1/16^n*(4/(8*n + 1) - 2/(8*n + 4) - 1/(8*n + 5) - 1/(8*n + 6)), {n, 0, 100}]] (* _G. C. Greubel_, Feb 18 2017 *)

%o (PARI) a(n)=numerator(1/16^n*(4/(8*n+1)-2/(8*n+4)-1/(8*n+5)-1/(8*n+6)))

%o (PARI) a(n)=numerator((1/16)^n*sum(i=1,4,((-1)^(ceil(4/(2*i))))*(floor(4/i))/(8*n+i+floor(sqrt(i-1))*(floor(sqrt(i-1))+1)))) \\ _Alexander R. Povolotsky_, Aug 31 2009

%Y Cf. A066968.

%K easy,frac,nonn,look

%O 0,1

%A _Benoit Cloitre_, Aug 13 2002