

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
The average length of chords in a unit square drawn between two points uniformly and independently chosen at random on two adjacent sides.  Amiram Eldar, Aug 08 2020


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. Bailey, J. Borwein, and R. Crandall, Advances in the theory of box integrals, Mathematics of Computation, Vol. 79, No. 271 (2010), pp. 18391866. See p. 1860.
Philip W. Kuchel and Rodney J. Vaughan, Average lengths of chords in a square, Mathematics Magazine, Vol. 54, No. 5 (1981), pp. 261269.
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 * A334380 A101464 A072558
Adjacent sequences: A244918 A244919 A244920 * A244922 A244923 A244924


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jul 08 2014


STATUS

approved



