A396610 Decimal expansion of the mean distance from the center to the interior points of a regular tetrahedron of unit volume.

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

Offset

0,1

Links

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

Index entries for sequences related to tetrahedron.

Formula

Equals (18*sqrt(3) - Pi + 15*sqrt(2)*arcsinh(sqrt(2)))/(48*3^(2/3)) (Dominik Beck, personal communication).

Example

0.524320131825907837202758555735459600145299743297348...

Mathematica

RealDigits[(18*Sqrt[3] - Pi + 15*Sqrt[2]*ArcSinh[Sqrt[2]])/(48*3^(2/3)), 10, 120][[1]]

Prog

(PARI) (18*sqrt(3) - Pi + 15*sqrt(2)*asinh(sqrt(2)))/(48*3^(2/3))

Crossrefs

Cf. A135691 (cube), this constant (tetrahedron), A396611 (octahedron), A396612 (dodecahedron), A396613 (icosahedron).

Cf. A366019.

Sequence in context: A372286 A368690 A083241 * A111145 A249920 A380200

Adjacent sequences: A396607 A396608 A396609 * A396611 A396612 A396613

Keyword

nonn,cons

Author

Amiram Eldar, May 31 2026

Status

approved