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

1,1

Comments

The biaugmented pentagonal prism is Johnson solid J_53.

Links

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

Wikipedia, Biaugmented pentagonal prism.

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.

Example

9.905056416315688432572916637788963932700358847641...

Mathematica

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

Crossrefs

Cf. A385534 (volume).

Cf. A002163, A010469, A385510.

Sequence in context: A302711 A021838 A199960 * A257176 A387444 A324859

Adjacent sequences: A385532 A385533 A385534 * A385536 A385537 A385538

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 03 2025

Status

approved