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

1,1

Comments

The augmented pentagonal prism is Johnson solid J_52.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Augmented pentagonal prism.

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.

Example

9.17300560874681113904547029628309156575755359383...

Mathematica

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

Crossrefs

Cf. A385509 (volume).

Cf. A002163, A002194.

Sequence in context: A280703 A364502 A141749 * A117017 A244861 A058969

Adjacent sequences: A385507 A385508 A385509 * A385511 A385512 A385513

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 02 2025

Status

approved