OFFSET
0,1
COMMENTS
Decimal expansion is A131917.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..9999
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
(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
3.73929751945... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(5 + 1/(11 + ...))))).
MATHEMATICA
ContinuedFraction[1/(1-EulerGamma-Log[3/2])-54, 100] (* Harvey P. Dale, Dec 18 2013 *)
PROG
(PARI) contfrac(1/(1 - Euler - log(3/2)) - 54) \\ Michel Marcus, Mar 11 2013
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(1/(1 - EulerGamma(R) - Log(3/2)) - 54); // G. C. Greubel, Aug 29 2018
CROSSREFS
KEYWORD
cofr,easy,nonn
AUTHOR
Jonathan Vos Post, Jul 27 2007
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 10 2024
STATUS
approved