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A086032 Decimal expansion of the Riemann zeta prime modulo function at 2 for primes of the form 4k+1. 3
0, 5, 3, 8, 1, 3, 7, 6, 3, 5, 7, 4, 0, 5, 7, 6, 7, 0, 2, 8, 0, 6, 7, 8, 2, 8, 7, 3, 4, 1, 5, 3, 6, 5, 6, 2, 2, 8, 5, 6, 7, 5, 5, 0, 1, 4, 9, 5, 0, 8, 5, 5, 3, 2, 2, 9, 3, 9, 1, 1, 4, 2, 2, 2, 9, 5, 8, 6, 6, 8, 2, 7, 0, 4, 4, 1, 4, 2, 6, 4, 5, 1, 4, 2, 5, 2, 6, 5, 5, 7, 5, 0, 4, 2, 3, 4, 3, 8, 9, 1, 2, 9, 2, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..104.

R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547, section 3.2 constant P(m=4,n=1,s=2).

X. Gourdon and P. Sebah, Some Constants from Number theory.

FORMULA

Zeta_Q(2) = Sum_{r prime=1 mod 4} 1/r^2= sum_{n>=1} 1/A002144(n)^2.

Equals A085548 -1/4 - A085991. - R. J. Mathar, Apr 03 2011

EXAMPLE

0.0538137635740576...

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 = 110; $MaxExtraPrecision = 320; Prepend[RealDigits[(1/2)* NSum[MoebiusMu[2n + 1]*Log[a[(2n + 1)*2]]/(2n + 1), {n, 0, m}, AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m]][[1]], 0][[1 ;; 105]] (* Jean-Fran├žois Alcover, Jun 24 2011, after X. Gourdon and P. Sebah *)

CROSSREFS

Cf. A085991.

Sequence in context: A019663 A187488 A087654 * A018222 A241149 A093203

Adjacent sequences:  A086029 A086030 A086031 * A086033 A086034 A086035

KEYWORD

cons,nonn

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 07 2003

STATUS

approved

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Last modified May 26 13:02 EDT 2017. Contains 287095 sequences.