A395017 Decimal expansion of the median of the distribution of distances between two points in the interior of a unit cube.

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

Offset

0,1

Comments

The smallest of the 4 roots of x^6/3 - 16*x^5/5 + 3*Pi*x^4 - 8*Pi*x^3/3 + 1 = 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.

Formula

0.662283184810160407091191336959903968193949829588101...

Mathematica

RealDigits[x /. FindRoot[x^6/3 - 16*x^5/5 + 3*Pi*x^4 - 8*Pi*x^3/3 + 1, {x, 1/2}, WorkingPrecision -> 120]][[1]]

Prog

(PARI) solve(x = 1/2, 1, x^6/3 - 16*x^5/5 + 3*Pi*x^4 - 8*Pi*x^3/3 + 1)

Crossrefs

Cf. A073012 (mean), A395018 (mode), A394606 (disk), A394608 (square), A395020 (ball), A395016.

Sequence in context: A191504 A396593 A021155 * A254245 A387610 A218387

Adjacent sequences: A395014 A395015 A395016 * A395018 A395019 A395020

Keyword

nonn,cons

Author

Amiram Eldar, Apr 10 2026

Status

approved