A232812 Decimal expansion of the surface index of a regular tetrahedron.

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

Offset: 1

Author

Stanislav Sykora, Dec 01 2013

Keywords

• nonn
• cons
• easy

Comments

Equivalently, the surface area of a regular tetrahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: this one, 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and A232809 (icosahedron).

Examples

			7.20562173105601636005279232409725707779044450935589335...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 6

Crossrefs

Cf. A002194, A020829, A232808 (surface index of a sphere), A232809, A232810, A232811.

Programs

Mathematica

RealDigits[2*Sqrt[3]*3^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

PARI

sqrtn(139968,6) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals 2*sqrt(3)*3^(2/3).

Equals A002194/A020829^(2/3).