OFFSET
0,1
COMMENTS
The same integral with 1/x instead of floor(1/x) evaluates to Pi^2/12 = A072691.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8 Khinchin-Lévy constants, p. 61.
LINKS
David Bailey, Jonathan Borwein and Richard Crandall, On the Khintchine constant, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 417-431.
Daniel Shanks and John W. Wrench, Jr., Khintchine's constant." The American Mathematical Monthly, Vol. 66, No. 4 (1959), pp. 276-279.
Eric Weisstein's MathWorld, Khinchin's Constant
FORMULA
Equals log(2)*log(K), where K is Khinchin's constant A002210 = 2.685452...
From Amiram Eldar, Aug 19 2020: (Start)
Equals Sum_{k>=1} (zeta(2*k)-1)/k * (1 - 1/2 + 1/3 - ... + 1/(2*k - 1)).
Equals -Sum_{k>=2} log(1-1/k) * log(1+1/k). (End)
EXAMPLE
0.6847247885631571232991461487557776204606754163374488366...
MATHEMATICA
RealDigits[Log[2]*Log[Khinchin], 10, 104] // First
PROG
(Python)
from mpmath import mp, log, khinchin
mp.dps=106
print([int(n) for n in list(str(log(2)*log(khinchin)))[2:-2]]) # Indranil Ghosh, Jul 08 2017
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 10 2014
STATUS
approved