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A254140
Decimal expansion of the average reciprocal distance between two points chosen at random in a unit square.
3
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
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved