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A086034 Decimal expansion of the Riemann zeta prime modulo function at 4 for primes of the form 4k+1. 1
0, 0, 1, 6, 4, 9, 5, 8, 4, 1, 5, 4, 0, 2, 9, 2, 9, 1, 5, 9, 8, 9, 9, 6, 7, 6, 1, 3, 1, 3, 6, 3, 8, 8, 5, 1, 8, 2, 7, 4, 8, 7, 9, 0, 9, 9, 4, 3, 8, 3, 4, 7, 3, 2, 1, 4, 7, 8, 1, 1, 5, 2, 5, 8, 3, 8, 8, 0, 0, 4, 9, 7, 5, 1, 7, 8, 7, 7, 7, 8, 8, 9, 3, 6, 8, 0, 1, 8, 2, 8, 0, 8, 7, 2, 2, 3, 0, 3, 6, 4, 6, 3, 9, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

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

FORMULA

Zeta_Q(4) = Sum_{r prime=1 mod 4} 1/r^4

EXAMPLE

0.0016495841540292...

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 = 680; Join[{0, 0}, RealDigits[(1/2)* NSum[MoebiusMu[2n + 1]*Log[a[(2n + 1)*4]]/(2n + 1), {n, 0, m}, AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m]][[1]]][[1 ;; 105]] (* Jean-Fran├žois Alcover, Jun 24 2011, after X. Gourdon and P. Sebah *)

CROSSREFS

Sequence in context: A195414 A153630 A113276 * A191622 A021943 A168198

Adjacent sequences:  A086031 A086032 A086033 * A086035 A086036 A086037

KEYWORD

cons,nonn

AUTHOR

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

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.