A395846 Decimal expansion of the expected distance between the center of a unit-side equilateral triangle to a randomly and uniformly selected point on its perimeter.

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

Offset

0,1

Links

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

Index entries for transcendental numbers.

Formula

Equals (2*sqrt(3) + arcsinh(sqrt(3)))/12.

Equals (2*sqrt(3) + log(2 + sqrt(3)))/12.

Example

0.398421626005214274639994919193309431492716039924023...

Mathematica

RealDigits[(2*Sqrt[3] + ArcSinh[Sqrt[3]])/12, 10, 120][[1]]

Prog

(PARI) (2*sqrt(3) + asinh(sqrt(3)))/12

Crossrefs

Cf. A065918, A093064, A245698, A245700, A345653 (square), A395847 (regular pentagon), A395848 (regular hexagon).

Sequence in context: A199052 A021255 A388573 * A388665 A394964 A388208

Adjacent sequences: A395843 A395844 A395845 * A395847 A395848 A395849

Keyword

nonn,cons

Author

Amiram Eldar, May 08 2026

Status

approved