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A131917
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Decimal expansion of 1 / (1 - gamma - log(3/2)) - 54, where gamma is the Euler-Mascheroni constant.
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4
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3, 7, 3, 9, 2, 9, 7, 5, 1, 9, 4, 5, 1, 1, 8, 4, 2, 0, 7, 3, 6, 6, 3, 3, 2, 8, 6, 9, 6, 8, 6, 1, 5, 1, 7, 2, 5, 6, 6, 2, 6, 3, 6, 8, 5, 4, 5, 6, 4, 1, 9, 2, 1, 7, 8, 3, 0, 7, 8, 9, 8, 1, 2, 1, 0, 0, 7, 9, 5, 7, 2, 3, 2, 6, 2, 0, 3, 5, 2, 5, 4, 5, 3, 0, 1, 7, 9, 7, 0, 9, 4, 2, 3, 7, 1, 7, 7, 6, 2, 2, 8, 5, 8, 3, 1
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OFFSET
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1,1
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COMMENTS
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Continued fraction expansion is given in A131918.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..10000
Mark B. Villarino, Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number, arXiv:0707.3950 [math.CA], 2007. Constant occurs in Theorem 7 (DeTemple-Wang), formula (1.14), page 6.
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FORMULA
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Equals (54 log(3/2) + 54 gamma - 53)/(1 - log(3/2) - gamma) = 1 / (1 - gamma - log(3/2)) - 54, where Martin Fuller simplifies the constant which Villarino showed was implicitly given by DeTemple and Wang.
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EXAMPLE
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3.739297519451184207366332869686151725662636854564...
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MATHEMATICA
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RealDigits[1/(1 - EulerGamma - Log[3/2]) - 54, 10, 100][[1]] (* G. C. Greubel, Aug 29 2018 *)
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PROG
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(PARI) 1/(1 - Euler - log(3/2)) - 54 \\ Michel Marcus, Mar 11 2013
(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); 1/(1 - EulerGamma(R) - Log(3/2)) - 54; // G. C. Greubel, Aug 29 2018
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CROSSREFS
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Cf. A001008, A001620, A131915, A131916, A131918.
Sequence in context: A309601 A201903 A133056 * A019785 A074176 A005596
Adjacent sequences: A131914 A131915 A131916 * A131918 A131919 A131920
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Vos Post, Jul 27 2007
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STATUS
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approved
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