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 A085995 Decimal expansion of the Riemann zeta prime modulo function at 6 for primes of the form 4k+3. 4
 0, 0, 1, 3, 8, 0, 8, 3, 5, 8, 8, 6, 9, 7, 1, 7, 3, 9, 1, 6, 3, 0, 3, 1, 8, 5, 4, 1, 2, 8, 0, 1, 5, 8, 2, 2, 6, 1, 0, 6, 0, 1, 3, 9, 6, 3, 2, 7, 5, 6, 5, 4, 2, 9, 6, 8, 0, 2, 6, 4, 8, 0, 2, 5, 7, 8, 5, 3, 0, 7, 5, 2, 2, 2, 7, 0, 7, 4, 6, 9, 1, 3, 4, 7, 9, 1, 5, 6, 0, 4, 2, 5, 1, 7, 1, 0, 1, 6, 6, 0, 1, 6, 8, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS P. Flajolet and I. Vardi, Zeta Function Expansions of Classical Constants, Unpublished manuscript. 1996. X. Gourdon and P. Sebah, Some Constants from Number theory. FORMULA Zeta_R(6) = Sum_{r prime=3 mod 4} 1/r^6 = (1/2)*Sum_{n=0..inf} mobius(2*n+1)*log(b((2*n+1)*6))/(2*n+1), where b(x)=(1-2^(-x))*zeta(x)/L(x) and L(x) is the Dirichlet Beta function. EXAMPLE 0.0013808358869717... MATHEMATICA b[x_] = (1 - 2^(-x))*(Zeta[x]/DirichletBeta[x]); \$MaxExtraPrecision = 250; m = 40; Join[{0, 0}, RealDigits[(1/2)*NSum[MoebiusMu[2n + 1]* Log[b[(2n + 1)*6]]/(2n + 1), {n, 0, m}, AccuracyGoal -> 120, NSumTerms -> m, PrecisionGoal -> 120, WorkingPrecision -> 120] ][[1]]][[1 ;; 105]] (* Jean-François Alcover, Jun 22 2011, updated Mar 14 2018 *) CROSSREFS Cf. A085991, A085992, A085993, A085994. Sequence in context: A154462 A112255 A197417 * A076482 A225802 A156827 Adjacent sequences:  A085992 A085993 A085994 * A085996 A085997 A085998 KEYWORD cons,nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003 STATUS approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)