A254140 Decimal expansion of the average reciprocal distance between two points chosen at random in a unit square.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

D. H. Bailey, J. M. Borwein, R. E. Crandall, Advances in the theory of box integrals Math. Comp. 79 (2010), 1839-1866, p. 24.

Eric Weisstein's MathWorld, Square Line Picking

Formula

Integral over a unit square of 1/sqrt((r1-q1)^2 + (r2-q2)^2) dr1 dr2 dq1 dq2 = 4/3 - 4*sqrt(2)/3 + 4*log(1 + sqrt(2)).

Example

2.97320959824737870252818566763957179801974547921061 ...

Mathematica

RealDigits[4/3 - 4*Sqrt[2]/3 + 4*Log[1 + Sqrt[2]], 10, 105] // First

Crossrefs

Cf. A091505.

Sequence in context: A230480 A335605 A308320 * A200991 A013500 A244596

Adjacent sequences: A254137 A254138 A254139 * A254141 A254142 A254143

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jan 26 2015

Status

approved