A348683 Decimal expansion of the average length of a chord in a unit cube defined by the intersection of the surface with a straight line passing through 2 points uniformly and independently chosen at random in the interior of the cube.

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

Offset

1,4

Links

Table of n, a(n) for n=1..105.

Rodney Coleman, Random paths through convex bodies, Journal of Applied Probability, Vol. 6, No. 2 (1969), pp. 430-441; alternative link; author's link.

Formula

Equals 4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3.

Example

1.10284530377862705859305188874735596957733355965158...

Mathematica

RealDigits[4/63 - Pi/9 + 17*Sqrt[2]/63 - 2*Sqrt[3]/21 + Log[1+Sqrt[2]]/3 + 2*Log[2+Sqrt[3]]/3, 10, 100][[1]]

Prog

(PARI) 4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3 \\ Michel Marcus, Oct 29 2021

Crossrefs

Cf. A073012, A093066, A348680, A348681, A348682.

Sequence in context: A227334 A105351 A178592 * A301389 A329452 A222238

Adjacent sequences: A348680 A348681 A348682 * A348684 A348685 A348686

Keyword

nonn,cons

Author

Amiram Eldar, Oct 29 2021

Status

approved