A344076 Decimal expansion of sqrt(61/2 + 18*sqrt(3) + 30*sqrt(1+sqrt(3)))/3.

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

Offset

1,1

Comments

The volume of a gyroelongated triangular cupola with unit edge length whose faces are all regular.

Links

Table of n, a(n) for n=1..93.

Polytope Wiki, Gyroelongated triangular cupola.

Eric Weisstein's World of Mathematics, Gyroelongated Triangular Cupola.

Wikipedia, Gyroelongated triangular cupola.

Index entries for algebraic numbers, degree 8.

Formula

Minimal polynomial: 104976*x^8 - 1423008*x^6 + 2381400*x^4 - 11448936*x^2 + 14190289. - Amiram Eldar, May 30 2026

Example

3.516053090938314468879...

Mathematica

RealDigits[Sqrt[61/2 + 18 Sqrt[3] + 30 Sqrt[1 + Sqrt[3]]]/3, 10, 200][[1]]

Prog

(PARI) sqrt(61/2+18*sqrt(3)+30*sqrt(1+sqrt(3)))/3 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A344077 (gyroelongated triangular cupola surface area).

Sequence in context: A076553 A199616 A173973 * A333336 A061649 A237603

Adjacent sequences: A344073 A344074 A344075 * A344077 A344078 A344079

Keyword

cons,nonn

Author

Wesley Ivan Hurt, May 08 2021

Status

approved