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A131917 Decimal expansion of 1 / (1 - gamma - log(3/2)) - 54, where gamma is the Euler-Mascheroni constant. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Continued fraction expansion is given in A131918.

LINKS

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.

FORMULA

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.

EXAMPLE

3.739297519451184207366332869686151725662636854564...

MATHEMATICA

RealDigits[1/(1 - EulerGamma - Log[3/2]) - 54, 10, 100][[1]] (* G. C. Greubel, Aug 29 2018 *)

PROG

(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

CROSSREFS

Cf. A001008, A001620, A131915, A131916, A131918.

Sequence in context: A309601 A201903 A133056 * A019785 A074176 A005596

Adjacent sequences:  A131914 A131915 A131916 * A131918 A131919 A131920

KEYWORD

cons,easy,nonn

AUTHOR

Jonathan Vos Post, Jul 27 2007

STATUS

approved

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Last modified June 30 03:34 EDT 2022. Contains 354913 sequences. (Running on oeis4.)