A116577 - OEIS

%I #3 Mar 31 2012 20:47:12

%S 0,2900288388,197346,5322158,128736743

%N Integer inverse of four parts of Pi by a Prime modulo 12 partition.

%C The method divides Pi into four irrational and one rational factor using the mapping of modulo 12 primes to the Integers. The result is the numerical approximation I can get with my Mathematica.

%F a(n) = Floor of inverse of Prime modulo 12 functions based on BBP {1,5,7,11}

%t q0 = 1/16^(n/2); t0 = 4/(8*n + 1); x0 = -2/(8*n + 4); y0 = -1/(8*n + 5); z0 = -1/(8*n + 6); f[n_] = q0^2*(x0 + y0 + z0 + t0) g[n_, 1] := If[Mod[Prime[n], 12] - 1 == 0, f[n], 0] g[n_, 2] := If[Mod[Prime[n], 12] - 5 == 0, f[n], 0] g[n_, 3] := If[Mod[Prime[n], 12] - 7 == 0, f[n], 0] g[n_, 4] := If[Mod[Prime[n], 12] - 11 == 0, f[n], 0] PiN[m_] := Sum[g[n, m], {n, 1, 10000}] Pi5 = Sum[f[n], {n, 0, 2}] aout = Flatten[{1/N[Pi5, 100], Table[1/N[PiN[n], 100], {n, 1, 4}]}] Floor[aout ]

%K nonn,uned,obsc

%O 0,2

%A _Roger L. Bagula_, Mar 21 2006