A131915 - OEIS

%I #24 Oct 28 2022 17:13:38

%S 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,

%T 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,

%U 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

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

%C Continued fraction expansion is A131916.

%H G. C. Greubel, <a href="/A131915/b131915.txt">Table of n, a(n) for n = 1..10000</a>

%H Mark B. Villarino, <a href="http://arXiv.org/abs/0707.3950">Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number</a>, arXiv:0707.3950 [math.CA], 2007. Constant occurs in Theorem 6, formula (1.13), page 6.

%F _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.

%e 1.1215093407317605227686154352944471024565027863162667052816...

%t RealDigits[1/(1-EulerGamma-Log[Sqrt[2]])-12,10,120][[1]] (* _Harvey P. Dale_, Mar 31 2012 *)

%o (PARI) 1/(1 - Euler - log(sqrt(2))) - 12 \\ _Michel Marcus_, Mar 11 2013

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 1/(1 - EulerGamma(R) - Log(Sqrt(2))) - 12; // _G. C. Greubel_, Aug 29 2018

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

%K cons,easy,nonn

%O 1,3

%A _Jonathan Vos Post_, Jul 27 2007