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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

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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: A228708 A191504 A021155 * A254245 A387610 A218387

Adjacent sequences: A395004 A395015 A395016 * A395018 A395019 A395020