A253191 Decimal expansion of log(2)^2.

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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, On the Khintchine Constant, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 417-431, see p. 419; alternative link, p. 4.

Index entries for transcendental numbers

Formula

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

Integral_{0..1} log(log(1/x))/(x+sqrt(x)) dx = log(2)^2.

Equals Sum_{k>=1} H(k)/(2^k * (k+1)) = 2 * Sum_{k>=1} (-1)^(k+1) * H(k)/(k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Aug 05 2020

Equals Sum_{n >= 0} (-1)^n/(2^(n+1)*(n+1)^2*binomial(2*n+1,n)). See my entry in A002544 dated Apr 18 2017. Cf. A091476. - Peter Bala, Jan 30 2023

Example

0.480453013918201424667102526326664971730552951594545586866864...

Mathematica

RealDigits[Log[2]^2, 10, 103] // First

Prog

(PARI) log(2)^2 \\ Charles R Greathouse IV, Apr 20 2016

Crossrefs

Cf. A001008, A002162, A002805, A175478.

Sequence in context: A185578 A087264 A342995 * A199777 A200389 A195455

Adjacent sequences: A253188 A253189 A253190 * A253192 A253193 A253194

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 24 2015

Status

approved