A396520 Decimal expansion of 16*(3 + 2*sqrt(3) - 4*sqrt(2))/3.

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

Offset

1,1

Comments

Volume of the solid created by the intersection of six cylinders with unit radius, with their longitudinal axes (all meeting at a single point) parallel to the face diagonals of a cube.

Links

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

Eric Weisstein's World of Mathematics, Steinmetz Solid.

Wikipedia, Steinmetz solid.

Index entries for algebraic numbers, degree 4.

Formula

Equals 16*(3 + A010469 - A010487)/3.

Equals the smallest positive root of 81*x^4 - 5184*x^3 - 78336*x^2 + 5160960*x - 20381696.

Example

4.3053192834419967565234015262557462379035893659358...

Mathematica

First[RealDigits[16*(3 + Sqrt[12] - Sqrt[32])/3, 10, 100]]

Crossrefs

Cf. volume of other cylinder intersections: A396517 (three cylinders), A396519 (four cylinders).

Cf. A010469, A010487.

Sequence in context: A388582 A204694 A304030 * A338802 A242721 A251610

Adjacent sequences: A396517 A396518 A396519 * A396521 A396522 A396523

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 31 2026

Status

approved