

A244921


Decimal expansion of (sqrt(2)+log(1+sqrt(2)))/3, the integral over the square [0,1]x[0,1] of sqrt(x^2+y^2) dx dy.


13



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

0,1


COMMENTS

This is also the expected distance from a randomly selected point in the unit square to a corner, as well as the expected distance from a randomly selected point in a 454590 degree triangle of base length 1 to a vertex with an acute angle.  Derek Orr, Jul 27 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. H. Bailey, J. M. Borwein, R. E. Crandall, Advances in the theory of box integrals (2010) p. 22.
Index entries for transcendental numbers


FORMULA

Also equals (sqrt(2) + arcsinh(1))/3.
This is also 2*A103712.  Derek Orr, Jul 27 2014


EXAMPLE

0.76519571646421269134476601639649679586594406787952782797665844888136988756...


MATHEMATICA

RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/3, 10, 104] // First


PROG

(PARI) (sqrt(2)+log(1+sqrt(2)))/3 \\ G. C. Greubel, Jul 05 2017


CROSSREFS

Cf. A244920.
Sequence in context: A069814 A198816 A196553 * A101464 A072558 A022963
Adjacent sequences: A244918 A244919 A244920 * A244922 A244923 A244924


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jul 08 2014


STATUS

approved



