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A074785
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Decimal expansion of -log(log(2)).
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10
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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Donald Knuth, The Art of Computer Programming, 3rd Edition, Volume 1. Boston: Addison-Wesley Professional (1997): 619, Table 1 of Appendix A.
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LINKS
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FORMULA
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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
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EXAMPLE
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log(log(2)) = -0.36651292058166432701243915823266946945...
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MATHEMATICA
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RealDigits[-Log[Log[2]], 10, 120][[1]] (* Harvey P. Dale, Nov 24 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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