A242588 Decimal expansion of the expected reciprocal Euclidean distance between two random points in the unit cube.

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

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, and R. E. Crandall, Advances in the theory of box integrals Math. Comp. 79 (2010), 1839-1866, p. 24.

Wolfgang Hackbusch, Direct Integration of the Newton Potential over Cubes, Computing, Vol. 68 (2002), 193-216; ResearchGate preprint.

Eric Weisstein's World of Mathematics, 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).

From Amiram Eldar, Mar 21 2026: (Start)

Equals 2 * A336274.

Equals A394467 + A394468 + A394469/3. (End)

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

Prog

(PARI) 2*(1/5*(sqrt(2) + 1 - 2*sqrt(3)) - log((sqrt(2) - 1)*(2 - sqrt(3))) - Pi/3) \\ Amiram Eldar, Mar 21 2026

Crossrefs

Cf. A073012, A097047, A135691, A336274, A394467, A394468, A394469.

Sequence in context: A387347 A197848 A224875 * A392501 A105193 A178678

Adjacent sequences: A242585 A242586 A242587 * A242589 A242590 A242591

Keyword

nonn,cons

Author

Jean-François Alcover, May 20 2014

Status

approved