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 A256779 Decimal expansion of the generalized Euler constant gamma(1,5). 10
 7, 3, 5, 9, 2, 0, 3, 9, 6, 8, 3, 1, 6, 1, 7, 5, 8, 4, 1, 8, 9, 2, 8, 9, 7, 2, 5, 8, 4, 4, 7, 5, 2, 8, 9, 3, 0, 5, 9, 9, 9, 7, 3, 8, 3, 9, 8, 7, 6, 2, 5, 0, 1, 7, 6, 5, 2, 6, 4, 2, 1, 5, 4, 5, 4, 3, 4, 8, 9, 1, 5, 3, 2, 7, 6, 7, 9, 2, 3, 7, 7, 5, 8, 3, 2, 8, 8, 7, 8, 9, 2, 4, 5, 2, 7, 8, 1, 5, 0, 3, 2, 2, 4, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134. FORMULA Equals EulerGamma/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2). Sum_{n>=0} (1/(5n+1) - 2/5*arctanh(5/(10n+7))). EXAMPLE 0.735920396831617584189289725844752893059997383987625... MATHEMATICA RealDigits[-Log[5]/5 - PolyGamma[1/5]/5, 10, 105] // First PROG (PARI) Euler/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2) \\ Michel Marcus, Apr 10 2015 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/10*Sqrt(1 + 2/Sqrt(5)) + Log(5)/20 + Sqrt(5)/10*Log((1 + Sqrt(5))/2); // G. C. Greubel, Aug 28 2018 CROSSREFS Cf. A001620 (EulerGamma), A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)). Sequence in context: A319531 A175452 A084714 * A030760 A201682 A021580 Adjacent sequences:  A256776 A256777 A256778 * A256780 A256781 A256782 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Apr 10 2015 STATUS approved

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Last modified October 23 22:42 EDT 2019. Contains 328378 sequences. (Running on oeis4.)