A048581 Numerators of b(n) = (1/16^n)*(4/(8*n+1) - 2/(8*n+4) - 1/(8*n+5) - 1/(8*n+6)).

47, 53, 829, 79, 857, 1901, 5273, 97, 1787, 5563, 4519, 4057, 19139, 743, 25681, 229, 3687, 18647, 8329, 3853, 51067, 28069, 20483, 335, 72791, 4379, 85093, 22901, 6557, 52673, 112577, 2501, 127759, 13571, 15989, 38083, 161003, 28319, 35813

Offset: 0

Author

Benoit Cloitre, Aug 13 2002

Keywords

• easy
• frac
• nonn
• look

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

Crossrefs

Cf. A066968.

Programs

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 *)

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

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