A306243 Decimal expansion of Sum_{n>=2} log(n)/n!.
6, 0, 3, 7, 8, 2, 8, 6, 2, 7, 9, 1, 4, 8, 7, 9, 8, 8, 4, 1, 6, 1, 8, 3, 8, 1, 0, 9, 8, 2, 4, 5, 0, 5, 4, 8, 3, 0, 4, 1, 7, 0, 1, 5, 3, 1, 6, 4, 9, 9, 1, 0, 2, 1, 7, 7, 2, 4, 1, 3, 2, 1, 1, 3, 8, 2, 2, 7, 2, 2, 8, 4, 1, 0, 0, 5, 2, 5, 5, 6, 9, 4, 7, 8, 2, 1, 3, 7, 5, 0, 2, 4, 6, 4, 9, 7, 1, 0, 8, 8
Offset: 0
Examples
0.6037828627914879884...
Links
- István Mező, Problem 11806, Problems and Solutions, The American Mathematical Monthly, Vol. 121, No. 10 (2014), p. 947; Parseval and Kummer, Solution to Problem 11806 by Omran Kouba, ibid., Vol. 123, No. 9 (2016), pp. 943-944.
Programs
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Mathematica
NSum[Log[n]/n!, {n, 2, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100] // RealDigits[#, 10, 100] & -
PARI
suminf(n=2, log(n)/n!) \\ Michel Marcus, Jan 31 2019
Formula
Equal to log(exp(1/2*log(2*exp(1/3*log(3*exp(1/4*log(4*exp(...)))))))).
Equals log(A296301). - Vaclav Kotesovec, Jun 22 2023
Equals Integral_{x=0..2*Pi} log(Gamma(x/(2*Pi))) * exp(cos(x)) * sin(x + sin(x)) dx - (e-1)*(log(2*Pi)+gamma), where gamma is Euler's constant (A001620) (Mező, 2014). - Amiram Eldar, Jan 25 2024
Equals Integral_{x=0..1} (exp(x) - 1)/(x*log(x)) - (exp(1) - 1)/log(x) dx. - Velin Yanev, Nov 29 2024