A395844 Decimal expansion of the expected distance of a point uniformly selected at random in the interior of a unit-side equilateral triangle to its farthest vertex.

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

Offset

0,1

Links

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

Eric Weisstein's World of Mathematics, Triangle Point Picking.

Index entries for transcendental numbers.

Formula

Equals (27*log(3) + sqrt(3)*(4 + 3*log(3)) - 6*sqrt(3)*arcsinh(sqrt(3)))/36.

Example

0.79480733322987534391386667022183944873388881213248...

Mathematica

RealDigits[(27*Log[3] + Sqrt[3]*(4 + 3*Log[3]) - 6*Sqrt[3]*ArcSinh[Sqrt[3]])/36, 10, 120][[1]]

Prog

(PARI) (27*log(3) + sqrt(3)*(4 + 3*log(3)) - 6*sqrt(3)*asinh(sqrt(3)))/36

Crossrefs

Cf. A065918, A093064, A245698, A245700, A395843, A395845 (square).

Sequence in context: A118270 A179292 A361972 * A198756 A140899 A201925

Adjacent sequences: A395841 A395842 A395843 * A395845 A395846 A395847

Keyword

nonn,cons

Author

Amiram Eldar, May 08 2026

Status

approved