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 A243265 Decimal expansion of the generalized Glaisher-Kinkelin constant A(5). 27
 1, 0, 0, 9, 6, 8, 0, 3, 8, 7, 2, 8, 5, 8, 6, 6, 1, 6, 1, 1, 2, 0, 0, 8, 9, 1, 9, 0, 4, 6, 2, 6, 3, 0, 6, 9, 2, 6, 0, 3, 2, 7, 6, 3, 4, 7, 2, 1, 1, 5, 2, 4, 9, 1, 8, 4, 6, 0, 9, 2, 4, 7, 2, 1, 5, 6, 2, 3, 0, 1, 4, 2, 5, 0, 0, 3, 4, 1, 0, 0, 3, 2, 7, 7, 0, 1, 5, 0, 5, 6, 5, 9, 6, 5, 2, 7, 6, 4, 5, 5, 5, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also known as the 5th Bendersky constant. REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137. LINKS G. C. Greubel, Table of n, a(n) for n = 1..2004 Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant FORMULA A(k) = exp(B(k+1)/(k+1)*H(k)-zeta'(-k)), where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number. A(5) = exp(137/15120-zeta'(-5)). Equals exp(gamma/252 - 15*Zeta'(6)/(4*Pi^6)) * (2*Pi)^(1/252), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015 EXAMPLE 1.00968038728586616112008919046263... MATHEMATICA RealDigits[Exp[137/15120-Zeta'[-5]], 10, 103] // First RealDigits[Exp[N[(BernoulliB[6]/6)*(EulerGamma + Log[2*Pi] - Zeta'[6]/Zeta[6]), 200]]]//First (* G. C. Greubel, Dec 31 2015 *) CROSSREFS Cf. A255344, A259070. Cf. A019727, A074962, A243262, A243263, A243264, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567. Sequence in context: A019643 A011012 A157989 * A248472 A306553 A011194 Adjacent sequences: A243262 A243263 A243264 * A243266 A243267 A243268 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Jun 02 2014 STATUS approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)