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A086037 Decimal expansion of the Riemann zeta prime modulo function at 7 for primes of the form 4k+1. 0
0, 0, 0, 0, 1, 2, 8, 1, 8, 4, 4, 8, 5, 9, 9, 7, 9, 5, 2, 6, 8, 2, 5, 1, 0, 2, 6, 5, 8, 2, 1, 6, 6, 5, 0, 7, 9, 3, 5, 8, 2, 0, 6, 0, 6, 7, 4, 9, 5, 6, 3, 3, 4, 4, 7, 9, 4, 3, 6, 2, 6, 5, 6, 9, 1, 4, 6, 8, 2, 1, 9, 4, 3, 9, 9, 4, 9, 5, 0, 8, 5, 2, 8, 5, 3, 2, 3, 8, 9, 5, 3, 4, 0, 5, 4, 6, 4, 2, 7, 4, 5, 3, 9, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

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

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

FORMULA

Zeta_Q(7) = Sum_{q prime=1 mod 4} 1/q^7.

EXAMPLE

0.0000128184485997...

MATHEMATICA

a[s_] = (1 + 2^-s)^-1* DirichletBeta[s] Zeta[s]/Zeta[2 s]; m = 120; $MaxExtraPrecision = 1200; Join[{0, 0, 0, 0}, RealDigits[(1/2)* NSum[MoebiusMu[2n + 1]*Log[a[(2n + 1)*7]]/(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, updated Mar 14 2018 *)

CROSSREFS

Sequence in context: A201763 A254277 A244688 * A199787 A165274 A221074

Adjacent sequences:  A086034 A086035 A086036 * A086038 A086039 A086040

KEYWORD

cons,nonn

AUTHOR

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

STATUS

approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)