OFFSET
0,1
COMMENTS
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
B. Gourevitch, L'univers de Pi
FORMULA
Sum_{k>=0} b(k) = Pi.
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
MATHEMATICA
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 *)
PROG
(PARI) a(n)=numerator(1/16^n*(4/(8*n+1)-2/(8*n+4)-1/(8*n+5)-1/(8*n+6)))
(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
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, Aug 13 2002
STATUS
approved