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A242588 Decimal expansion of the expected reciprocal Euclidean distance between two random points in the unit cube. 1
1, 8, 8, 2, 3, 1, 2, 6, 4, 4, 3, 8, 9, 6, 6, 0, 1, 6, 0, 1, 0, 5, 6, 0, 0, 8, 3, 8, 8, 6, 8, 3, 6, 7, 5, 8, 7, 8, 5, 2, 4, 6, 2, 8, 8, 0, 3, 1, 0, 7, 0, 7, 9, 6, 0, 5, 5, 2, 9, 3, 2, 3, 1, 4, 5, 7, 7, 2, 1, 0, 3, 7, 9, 6, 1, 0, 6, 0, 3, 5, 8, 1, 2, 7, 2, 3, 9, 9, 9, 9, 1, 4, 8, 4, 5, 6, 2, 0, 4, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1, p. 480.

LINKS

Table of n, a(n) for n=1..100.

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, Cube Point Picking

FORMULA

Integral over a unit cube of 1/sqrt((r1-q1)^2 + (r2-q2)^2 + (r3-q3)^2) dr1 dr2 dr3 dq1 dq2 dq3 = 2*(1/5*(sqrt(2) + 1 - 2*sqrt(3)) - log((sqrt(2) - 1)*(2 - sqrt(3))) - Pi/3).

EXAMPLE

1.88231264438966016010560083886836758785246288...

MATHEMATICA

2*(1/5*(Sqrt[2] + 1 - 2*Sqrt[3]) - Log[(Sqrt[2] - 1)*(2 - Sqrt[3])] - Pi/3) // RealDigits[#, 10, 100]& // First

CROSSREFS

Cf. A073012, A097047, A135691.

Sequence in context: A199597 A197848 A224875 * A105193 A178678 A217459

Adjacent sequences: A242585 A242586 A242587 * A242589 A242590 A242591

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, May 20 2014

STATUS

approved

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Last modified December 2 14:15 EST 2022. Contains 358510 sequences. (Running on oeis4.)