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 A085993 Decimal expansion of the Riemann zeta prime modulo function at 4 for primes of the form 4k+3. 6
 0, 1, 2, 8, 4, 3, 5, 5, 5, 6, 1, 0, 2, 1, 7, 5, 5, 3, 3, 4, 3, 6, 2, 2, 5, 3, 4, 6, 1, 9, 5, 1, 9, 0, 1, 8, 3, 3, 4, 5, 5, 3, 1, 4, 9, 7, 7, 1, 0, 0, 8, 4, 5, 8, 1, 1, 7, 1, 2, 6, 4, 8, 3, 0, 2, 0, 4, 1, 6, 0, 7, 2, 9, 6, 9, 6, 8, 6, 4, 1, 7, 5, 7, 3, 5, 3, 1, 2, 7, 8, 6, 9, 8, 1, 7, 3, 2, 5, 3, 0, 7, 8, 0, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS P. Flajolet and I. Vardi, Zeta Function Expansions of Classical Constants, Unpublished manuscript. 1996.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(4) = Sum_{r prime=3 mod 4} 1/r^4 = (1/2)*Sum_{n=0..inf} mobius(2*n+1)*log(b((2*n+1)*4))/(2*n+1), where b(x)=(1-2^(-x))*zeta(x)/L(x) and L(x) is the Dirichlet Beta function. EXAMPLE 0.0128435556102175... MATHEMATICA b[x_] = (1 - 2^(-x))*(Zeta[x]/DirichletBeta[x]); \$MaxExtraPrecision = 200; m = 40; Prepend[ RealDigits[ (1/2)*NSum[ MoebiusMu[2n+1]* Log[b[(2n+1)*4]]/(2n+1), {n, 0, m}, AccuracyGoal -> 120, NSumTerms -> m, PrecisionGoal -> 120, WorkingPrecision -> 120] ][[1]], 0][[1 ;; 105]] (* Jean-François Alcover, Jun 22 2011, updated Mar 14 2018 *) CROSSREFS Cf. A085991, A085992. Sequence in context: A152626 A093823 A088154 * A010595 A109594 A329661 Adjacent sequences:  A085990 A085991 A085992 * A085994 A085995 A085996 KEYWORD cons,nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003 STATUS approved

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Last modified February 21 18:05 EST 2020. Contains 332107 sequences. (Running on oeis4.)