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A131916
Continued fraction expansion of 1 / (1 - gamma - log(sqrt(2))) - 12, where gamma is the Euler-Mascheroni constant.
4
1, 8, 4, 2, 1, 5, 1, 1, 5, 1, 1, 3, 8, 1, 4, 2, 6, 9, 5, 97, 2, 1, 1, 2, 9, 8, 5, 3, 16, 1, 31, 2, 1, 8, 7, 1, 2, 1, 15, 1, 1, 1, 3, 1, 12, 3, 11, 2, 1, 1, 13, 1, 3, 6, 1, 15, 9, 3, 4, 1, 2, 1, 5, 1, 1, 1, 18, 2, 5, 8, 1, 3, 1, 1, 2, 3, 12, 1, 8, 1, 2, 1, 1, 1, 2, 17, 13, 3, 1, 1, 1, 5, 1, 1, 3, 2, 1, 2, 3
OFFSET
0,2
COMMENTS
Decimal expansion is A131915.
LINKS
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(2^0.5))) / (1 - gamma - log(2^0.5)) or more simply: 1 / (1 - gamma - log(2^0.5)) - 12.
EXAMPLE
1.1215093407... = 1 + 1/(8 + 1/(4 + 1/(2 + 1/(1 + 1/(5 + ...))))).
MATHEMATICA
ContinuedFraction[1/(1-EulerGamma-Log[Sqrt[2]])-12, 100] (* Harvey P. Dale, Oct 01 2015 *)
PROG
(PARI) contfrac(1/(1 - Euler - log(sqrt(2))) - 12) \\ Michel Marcus, Mar 11 2013
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(1/(1 - EulerGamma(R) - Log(Sqrt(2))) - 12); // G. C. Greubel, Aug 29 2018
CROSSREFS
Cf. A001008, A001620, A131915 (decimal expansion), A131917, A131918.
Sequence in context: A197477 A133839 A080828 * A131606 A033328 A097529
KEYWORD
cofr,easy,nonn
AUTHOR
Jonathan Vos Post, Jul 27 2007
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 10 2024
STATUS
approved