A222067 Decimal expansion of 1/(8*sqrt(3)).

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

Offset

-1,1

Comments

Conjectured to be center density of densest packing of equal spheres in six dimensions (achieved for example by the E_6 lattice).

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.

Links

Table of n, a(n) for n=-1..102.

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.

G. Nebe and N. J. A. Sloane, Home page for E_6 lattice.

N. J. A. Sloane and Andrey Zabolotskiy, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).

Index entries for algebraic numbers, degree 2

Example

0.07216878364870322056364359756274468195595021890876585950232529...

Mathematica

RealDigits[1/(8*Sqrt[3]), 10, 120][[1]] (* Amiram Eldar, Jun 19 2023 *)

Prog

(PARI) 1/sqrt(192) \\ Charles R Greathouse IV, Oct 31 2014

Crossrefs

Related constants: A020769, A020789, A093766, A093825, A222066, A222068, A222069, A222070, A222071, A222072, A260646.

Sequence in context: A133362 A317925 A010140 * A154020 A060991 A120455

Adjacent sequences: A222064 A222065 A222066 * A222068 A222069 A222070

Keyword

nonn,cons,easy

Author

N. J. A. Sloane, Feb 10 2013

Extensions

Offset corrected by Georg Fischer, Aug 18 2022

Status

approved