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

Author

N. J. A. Sloane, Feb 10 2013

Keywords

• nonn
• cons

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

Examples

			.25366950790104801363656336637683622721283225435595161898819...
		

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

• 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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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