A131917 Decimal expansion of 1 / (1 - gamma - log(3/2)) - 54, where gamma is the Euler-Mascheroni constant.

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

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