A242053 Decimal expansion of 1/log(2)-1, the mean value of a random variable following the Gauss-Kuzmin distribution.

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

Offset: 0

Author

Jean-François Alcover, Aug 13 2014

Keywords

• nonn
• cons
• easy

Examples

			0.4426950408889634073599246810018921374266459541529859341354494...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.17 Gauss-Kuzmin-Wirsing constant, p. 151.

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, 2.17 p. 21.
• Michael Penn, This infinite series is crazy!, YouTube video, 2020.
• Index entries for transcendental numbers

Crossrefs

Cf. A007525.

Programs

Mathematica

RealDigits[1/Log[2] - 1, 10, 99] // First

Formula

Equals (1/log(2))*Integral_{x=0..1} x/(1+x) dx.

Equals Sum_{k>=1} 1/(2^k*(1 + 2^(2^(-k)))). - Amiram Eldar, May 28 2021