|
| |
|
|
A086036
|
|
Decimal expansion of the Riemann zeta prime modulo function at 6 for primes of the form 4k+1.
|
|
0
| |
|
|
0, 0, 0, 0, 6, 4, 2, 5, 0, 9, 6, 3, 6, 6, 4, 7, 7, 3, 7, 9, 1, 1, 0, 1, 8, 1, 9, 1, 3, 8, 0, 4, 3, 5, 7, 6, 5, 9, 8, 9, 8, 4, 5, 4, 5, 5, 4, 6, 9, 7, 8, 8, 1, 5, 0, 5, 2, 8, 9, 8, 5, 6, 6, 2, 5, 8, 4, 3, 8, 9, 8, 4, 5, 2, 0, 0, 9, 7, 7, 4, 5, 3, 2, 3, 9, 4, 4, 7, 4, 5, 8, 2, 6, 4, 7, 0, 4, 5, 7, 0, 1, 1, 9, 4, 4
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
LINKS
| X. Gourdon and P. Sebah, Some Constants from Number theory.
|
|
|
FORMULA
| Zeta_Q(6) = Sum_{q prime=1 mod 4} 1/q^6
|
|
|
EXAMPLE
| 0.0000642509636647...
|
|
|
MATHEMATICA
| DirichletBeta[s_] = (Zeta[s, 1/4] - Zeta[s, 3/4])/4^s;
a[s_] = (1 + 2^-s)^-1* DirichletBeta[s] Zeta[s]/Zeta[2 s]; m = 120; $MaxExtraPrecision = 1020;
Join[{0, 0, 0, 0}, RealDigits[(1/2)* NSum[MoebiusMu[2n + 1]*Log[a[(2n + 1)*6]]/(2n + 1), {n, 0, m},
AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m]][[1]]][[1 ;; 105]]
(* From J.F.Alcover, Jun 24 2011, after X. Gourdon and P. Sebah *)
|
|
|
CROSSREFS
| Sequence in context: A028975 A145011 A173625 * A019849 A118421 A158233
Adjacent sequences: A086033 A086034 A086035 * A086037 A086038 A086039
|
|
|
KEYWORD
| cons,nonn
|
|
|
AUTHOR
| Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 07 2003
|
| |
|
|
