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A074785 Decimal expansion of -log(log(2)). 10
3, 6, 6, 5, 1, 2, 9, 2, 0, 5, 8, 1, 6, 6, 4, 3, 2, 7, 0, 1, 2, 4, 3, 9, 1, 5, 8, 2, 3, 2, 6, 6, 9, 4, 6, 9, 4, 5, 4, 2, 6, 3, 4, 4, 7, 8, 3, 7, 1, 0, 5, 2, 6, 3, 0, 5, 3, 6, 7, 7, 7, 1, 3, 6, 7, 0, 5, 6, 1, 6, 1, 5, 3, 1, 9, 3, 5, 2, 7, 3, 8, 5, 4, 9, 4, 5, 5, 8, 2, 2, 8, 5, 6, 6, 9, 8, 9, 0, 8, 3, 5, 8, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The function f(p) = Integral_{x = 2..infinity} 1/(x*log(x)^p) has a minimum of -e*log(log(2)) = 0.996285... at p = 1 - 1/log(log(2)) = 3.728416... - Jean-François Alcover, May 24 2013
log(log(2)) also equals the median of the Gumbel distribution with location parameter 0 and scale parameter 1. - Jean-François Alcover, Jul 29 2014
REFERENCES
Donald Knuth, The Art of Computer Programming, 3rd Edition, Volume 1. Boston: Addison-Wesley Professional (1997): 619, Table 1 of Appendix A.
LINKS
Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to Pi^(-1), Journal of Mathematical Analysis and Applications, Vol. 442, No. 2 (2016), pp. 404-434.
Dmitrii Kouznetsov and Henryk Trappmann, Portrait of the four regular super-exponentials to base sqrt(2), Math. Comp., Vol. 79, No. 271 (2010), pp. 1727-1756, eq. (3.2).
Simon Plouffe, log(log(2)).
Eric Weisstein's World of Mathematics, Gumbel Distribution.
FORMULA
Equals Sum_{n>=1} ((-1)^n/(n*n!) * (Sum_{k=1..n} abs(S1(n,k))/(k+1))), where S1(n,k) are the Stirling numbers of the first kind (Blagouchine, 2016). Without the absolute value the formula gives -gamma (= -A001620). - Amiram Eldar, Jun 12 2021
EXAMPLE
log(log(2)) = -0.36651292058166432701243915823266946945...
MATHEMATICA
RealDigits[-Log[Log[2]], 10, 120][[1]] (* Harvey P. Dale, Nov 24 2013 *)
PROG
(PARI) -log(log(2)) \\ Charles R Greathouse IV, Jan 04 2016
CROSSREFS
Sequence in context: A185735 A339021 A197263 * A225462 A179949 A187601
KEYWORD
cons,easy,nonn
AUTHOR
Benoit Cloitre, Sep 07 2002
STATUS
approved

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Last modified March 2 12:34 EST 2024. Contains 370467 sequences. (Running on oeis4.)