|
|
A048581
|
|
Numerators of b(n) = (1/16^n)*(4/(8*n+1) - 2/(8*n+4) - 1/(8*n+5) - 1/(8*n+6)).
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|