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A086038
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Decimal expansion of the Riemann zeta prime modulo function at 8 for primes of the form 4k+1.
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0
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0, 0, 0, 0, 0, 2, 5, 6, 1, 3, 7, 1, 6, 8, 0, 3, 9, 6, 4, 6, 9, 8, 0, 8, 2, 4, 8, 4, 3, 2, 3, 1, 2, 4, 7, 3, 9, 3, 6, 4, 4, 7, 2, 6, 0, 6, 0, 1, 8, 0, 7, 2, 9, 8, 8, 7, 0, 6, 6, 6, 7, 5, 4, 5, 9, 9, 1, 7, 4, 7, 4, 1, 2, 1, 1, 1, 8, 8, 8, 4, 8, 9, 3, 8, 8, 9, 7, 9, 8, 9, 1, 4, 8, 1, 7, 8, 0, 3, 0, 3, 0, 1, 3, 7, 6
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..104.
X. Gourdon and P. Sebah, Some Constants from Number theory.
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FORMULA
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Zeta_Q(8) = Sum_{q prime=1 mod 4} 1/q^8
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EXAMPLE
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0.0000025613716803...
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MATHEMATICA
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a[s_] = (1 + 2^-s)^-1* DirichletBeta[s] Zeta[s]/Zeta[2 s]; m = 120; $MaxExtraPrecision = 1200; Join[{0, 0, 0, 0, 0}, RealDigits[(1/2)* NSum[MoebiusMu[2n + 1]*Log[a[(2n + 1)*8]]/(2n + 1), {n, 0, m}, AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m]][[1]]][[1 ;; 105]] (* Jean-François Alcover, Jun 24 2011, after X. Gourdon and P. Sebah, updated Mar 14 2018 *)
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CROSSREFS
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Sequence in context: A004650 A138279 A131800 * A200136 A134387 A222132
Adjacent sequences: A086035 A086036 A086037 * A086039 A086040 A086041
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KEYWORD
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cons,nonn
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 07 2003
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STATUS
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approved
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