A385535 Decimal expansion of the surface area of a biaugmented pentagonal prism with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 03 2025

Keywords

• nonn
• cons
• easy

Comments

The biaugmented pentagonal prism is Johnson solid J_53.

Examples

			9.905056416315688432572916637788963932700358847641...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Biaugmented pentagonal prism.

Crossrefs

Cf. A385534 (volume).

Cf. A002163, A010469, A385510.

Programs

Mathematica

First[RealDigits[3 + Sqrt[12] + Sqrt[25/4 + 5*Sqrt[5]/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J53", "SurfaceArea"], 10, 100]]

Formula

Equals 3 + 2*sqrt(3) + sqrt(25/4 + 5*sqrt(5)/2) = 3 + A010469 + sqrt(25/4 + 5*A002163/2).

Equals the largest root of 256*x^8 - 6144*x^7 + 45824*x^6 - 50688*x^5 - 729376*x^4 + 2504064*x^3 - 583184*x^2 - 4746912*x + 1628761.