A386739 Decimal expansion of the volume of a sphenocorona with unit edges.

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

Offset

1,2

Comments

The sphenocorona is Johnson solid J_86.

Links

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

Wikipedia, Sphenocorona.

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 = sqrt(1 + 3*A115754 + sqrt(13 + A010507))/2.

Equals A386740 - A020775.

Equals the largest real root of 1024*x^8 - 1024*x^6 - 3008*x^4 - 96*x^2 + 9.

Example

1.5153516399764065597284793124718129048228695068...

Mathematica

First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J86", "Volume"], 10, 100]]

Prog

(PARI) sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 \\ Charles R Greathouse IV, Nov 17 2025

Crossrefs

Cf. A010482 (surface area - 2), A178809 (surface area + 4).

Cf. A010507, A020775, A115754, A386740, A386741.

Sequence in context: A217774 A060186 A240995 * A122002 A322602 A228639

Adjacent sequences: A386736 A386737 A386738 * A386740 A386741 A386742

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 01 2025

Status

approved