A131915 Decimal expansion of 1 / (1 - gamma - log(sqrt(2))) - 12, where gamma is the Euler-Mascheroni constant.

1, 1, 2, 1, 5, 0, 9, 3, 4, 0, 7, 3, 1, 7, 6, 0, 5, 2, 2, 7, 6, 8, 6, 1, 5, 4, 3, 5, 2, 9, 4, 4, 4, 7, 1, 0, 2, 4, 5, 6, 5, 0, 2, 7, 8, 6, 3, 1, 6, 2, 6, 6, 7, 0, 5, 2, 8, 1, 6, 0, 6, 7, 2, 1, 9, 9, 4, 9, 0, 7, 5, 6, 2, 6, 5, 2, 2, 3, 4, 6, 6, 7, 6, 9, 1, 3, 5, 0, 0, 4, 0, 9, 1, 5, 5, 7, 0, 0, 2, 1, 8, 7, 7, 5, 5

Offset

1,3

Comments

Continued fraction expansion is A131916.

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 6, formula (1.13), page 6.

Formula

Martin Fuller corrected a typo in the cited paper. It should be: ((12 * gamma) - 11 + (12 * log(sqrt(2)))) / (1 - gamma - log(sqrt(2))) or more simply: 1 / (1 - gamma - log(sqrt(2))) - 12.

Example

1.1215093407317605227686154352944471024565027863162667052816...

Mathematica

RealDigits[1/(1-EulerGamma-Log[Sqrt[2]])-12, 10, 120][[1]] (* Harvey P. Dale, Mar 31 2012 *)

Prog

(PARI) 1/(1 - Euler - log(sqrt(2))) - 12 \\ Michel Marcus, Mar 11 2013
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 1/(1 - EulerGamma(R) - Log(Sqrt(2))) - 12; // G. C. Greubel, Aug 29 2018

Crossrefs

Cf. A001008, A001620, A131916, A131917, A131918.

Sequence in context: A021827 A338554 A317301 * A078036 A369865 A175178

Adjacent sequences: A131912 A131913 A131914 * A131916 A131917 A131918

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Jul 27 2007

Status

approved