A116577 Integer inverse of four parts of Pi by a Prime modulo 12 partition.

0, 2900288388, 197346, 5322158, 128736743

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..4.

Formula

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

Mathematica

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 ]

Crossrefs

Sequence in context: A257913 A346495 A072017 * A067615 A204338 A185889

Adjacent sequences: A116574 A116575 A116576 * A116578 A116579 A116580

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Mar 21 2006

Status

approved