A344149 Decimal expansion of 30+5*sqrt(3)+3*sqrt(25+10*sqrt(5)).

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

Offset

2,1

Comments

Decimal expansion of the surface area of a rhombicosidodecahedron with unit edge length.

Apart from the first digit the same as A179451. - R. J. Mathar, May 16 2021

Links

Table of n, a(n) for n=2..102.

Polytope Wiki, Small rhombicosidodecahedron.

Eric Weisstein's World of Mathematics, Rhombicosidodecahedron.

Wikipedia, Rhombicosidodecahedron.

Index entries for algebraic numbers, degree 8.

Formula

Minimal polynomial: x^8 - 240*x^7 + 24000*x^6 - 1296000*x^5 + 40824000*x^4 - 751680000*x^3 + 7554600000*x^2 - 33372000000*x + 19764000000. - Amiram Eldar, May 28 2026

Example

59.305982844911989540745375436192677...

Mathematica

RealDigits[N[30 + 5*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]], 100]][[1]] (* Wesley Ivan Hurt, Nov 12 2022 *)

Prog

(Magma) SetDefaultRealField(RealField(200)); 30+5*Sqrt(3)+3*Sqrt(25+10*Sqrt(5));
(PARI) 30+5*sqrt(3)+3*sqrt(25+10*sqrt(5)) \\ Charles R Greathouse IV, May 18 2026
(PARI) polrootsreal(x^8 - 240*x^7 + 24000*x^6 - 1296000*x^5 + 40824000*x^4 - 751680000*x^3 + 7554600000*x^2 - 33372000000*x + 19764000000)[8] \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A185093 (rhombicosidodecahedron volume), A179451.

Sequence in context: A377420 A111698 A216755 * A255681 A398082 A021948

Adjacent sequences: A344146 A344147 A344148 * A344150 A344151 A344152

Keyword

nonn,cons

Author

Wesley Ivan Hurt, May 10 2021

Status

approved