A384138 Decimal expansion of the volume of an elongated pentagonal pyramid with unit edge.

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

Offset

1,1

Comments

The elongated pentagonal pyramid is Johnson solid J_9.

Links

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

Wikipedia, Elongated pentagonal pyramid.

Index entries for algebraic numbers, degree 4.

Formula

Equals (5 + sqrt(5) + 6*sqrt(25 + 10*sqrt(5)))/24 = (5 + A002163 + 6*sqrt(25 + 10*A002163))/24.

Equals the largest root of 20736*x^4 - 17280*x^3 - 59760*x^2 + 15600*x + 9025.

Example

2.0219802329847914934427275469190794425507332683273...

Mathematica

First[RealDigits[(5 + Sqrt[5] + 6*Sqrt[25 + 10*Sqrt[5]])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J9", "Volume"], 10, 100]]

Crossrefs

Cf. A179553 (surface area - 5).

Cf. A002163, A383852, A384139, A384140.

Sequence in context: A298141 A160210 A174610 * A375108 A373924 A028928

Adjacent sequences: A384135 A384136 A384137 * A384139 A384140 A384141

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 20 2025

Status

approved