A385510 Decimal expansion of the surface area of an augmented pentagonal prism with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 02 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented pentagonal prism is Johnson solid J_52.

Examples

			9.17300560874681113904547029628309156575755359383...
		

Links

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

Crossrefs

Cf. A385509 (volume).

Cf. A002163, A002194.

Programs

Mathematica

First[RealDigits[4 + Sqrt[3] + Sqrt[25/4 + 5*Sqrt[5]/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J52", "SurfaceArea"], 10, 100]]

Formula

Equals 4 + sqrt(3) + sqrt(25/4 + 5*sqrt(5)/2) = 4 + A002194 + sqrt(25/4 + 5*A002163/2).

Equals the largest root of 256*x^8 - 8192*x^7 + 105216*x^6 - 690176*x^5 + 2391264*x^4 - 3788288*x^3 + 193904*x^2 + 6427776*x - 5201159.