A222072 Decimal expansion of (1/384)*Pi^4.

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

Offset

0,1

Comments

Conjectured to be density of densest packing of equal spheres in 8 dimensions (achieved for example by the E_8 lattice).

The above conjecture is true (cf. Viazovska, 2017). - Felix Fröhlich, Jan 08 2018

References

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

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.

Links

Table of n, a(n) for n=0..101.

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete & Computational Geometry, Vol. 13, No. 3-4 (1995), 383-403.

G. Nebe and N. J. A. Sloane, Home page for E_8 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).

Maryna S. Viazovska, The sphere packing problem in dimension 8, Annals of Mathematics, Vol. 185, No. 3 (2017), 991-1015.

Maryna S. Viazovska, The sphere packing problem in dimension 8, arXiv:1603.04246 [math.NT], 2017.

Index entries for transcendental numbers.

Formula

Equals Sum_{n>=1} Sum_{k>=n} 1/(2*n - 1)^2/(2*k + 1)^2. - Geoffrey Critzer, Nov 03 2013

Example

.25366950790104801363656336637683622721283225435595161898819...

Mathematica

RealDigits[Pi^4/ 384, 10, 120][[1]] (* Harvey P. Dale, Aug 11 2015 *)

Prog

(PARI) Pi^4/384 \\ Charles R Greathouse IV, Oct 31 2014

Crossrefs

Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A260646.

Sequence in context: A341492 A264105 A024871 * A246007 A256997 A335499

Adjacent sequences: A222069 A222070 A222071 * A222073 A222074 A222075

Keyword

nonn,cons

Author

N. J. A. Sloane, Feb 10 2013

Status

approved