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A131915 Decimal expansion of 1 / (1 - gamma - log(sqrt(2))) - 12, where gamma is the Euler-Mascheroni constant. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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]] (* From 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 A175178 A348494

Adjacent sequences:  A131912 A131913 A131914 * A131916 A131917 A131918

KEYWORD

cons,easy,nonn

AUTHOR

Jonathan Vos Post, Jul 27 2007

STATUS

approved

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Last modified May 17 11:26 EDT 2022. Contains 353745 sequences. (Running on oeis4.)