A395018 Decimal expansion of the mode of the distribution of distances between two points in the interior of a unit cube.

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

Offset

0,1

Comments

The second of the 4 roots of 5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x = 0.

Links

Table of n, a(n) for n=0..104.

Arak M. Mathai, Peter Moschopoulos, and Giorgio Pederzoli, Distance between random points in a cube, Statistica, Vol. 59, No. 1 (1999), pp. 61-81; ResearchGate link.

Eric Weisstein's World of Mathematics, Cube Line Picking.

Index entries for transcendental numbers.

Example

0.675230751991264244633196900774754334312565525608912...

Mathematica

RealDigits[x /. FindRoot[5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x, {x, 1/2}, WorkingPrecision -> 120]][[1]]

Prog

(PARI) solve(x = 1/2, 1, 5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x)

Crossrefs

Cf. A073012 (mean), A395017 (median), A394605 (disk), A394607 (square), A395019 (ball), A395016.

Sequence in context: A332396 A100124 A355336 * A390931 A190648 A201519

Adjacent sequences: A395015 A395016 A395017 * A395019 A395020 A395021

Keyword

nonn,cons

Author

Amiram Eldar, Apr 10 2026

Status

approved