A247038 Decimal expansion of Integral_{x=0..1} log(floor(1/x))/(1+x) dx.

6, 8, 4, 7, 2, 4, 7, 8, 8, 5, 6, 3, 1, 5, 7, 1, 2, 3, 2, 9, 9, 1, 4, 6, 1, 4, 8, 7, 5, 5, 7, 7, 7, 6, 2, 0, 4, 6, 0, 6, 7, 5, 4, 1, 6, 3, 3, 7, 4, 4, 8, 8, 3, 6, 6, 0, 6, 2, 8, 9, 8, 6, 7, 8, 1, 5, 9, 5, 6, 8, 8, 2, 1, 7, 6, 2, 6, 9, 3, 6, 1, 0, 4, 3, 7, 0, 7, 6, 8, 1, 4, 3, 4, 9, 5, 8, 5, 8, 1, 0, 0, 9, 9, 7

Offset: 0

Author

Jean-François Alcover, Sep 10 2014

Keywords

• nonn
• cons
• easy

Comments

The same integral with 1/x instead of floor(1/x) evaluates to Pi^2/12 = A072691.

Examples

			0.6847247885631571232991461487557776204606754163374488366...
		

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

Crossrefs

Cf. A002210, A072691.

Programs

Mathematica

RealDigits[Log[2]*Log[Khinchin], 10, 104] // First

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

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)