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%I #31 Dec 30 2023 08:31:23
%S 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,
%T 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,
%U 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
%N Decimal expansion of (1/384)*Pi^4.
%C Conjectured to be density of densest packing of equal spheres in 8 dimensions (achieved for example by the E_8 lattice).
%C The above conjecture is true (cf. Viazovska, 2017). - _Felix Fröhlich_, Jan 08 2018
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/BF02574051">What are all the best sphere packings in low dimensions?</a>, Discrete & Computational Geometry, Vol. 13, No. 3-4 (1995), 383-403.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/E8.html">Home page for E_8 lattice</a>
%H N. J. A. Sloane and Andrey Zabolotskiy, <a href="/A093825/a093825_1.txt">Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).</a>
%H Maryna S. Viazovska, <a href="https://doi.org/10.4007/annals.2017.185.3.7">The sphere packing problem in dimension 8</a>, Annals of Mathematics, Vol. 185, No. 3 (2017), 991-1015.
%H Maryna S. Viazovska, <a href="https://arxiv.org/abs/1603.04246">The sphere packing problem in dimension 8</a>, arXiv:1603.04246 [math.NT], 2017.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Sum_{n>=1} Sum_{k>=n} 1/(2*n - 1)^2/(2*k + 1)^2. - _Geoffrey Critzer_, Nov 03 2013
%e .25366950790104801363656336637683622721283225435595161898819...
%t RealDigits[Pi^4/ 384,10,120][[1]] (* _Harvey P. Dale_, Aug 11 2015 *)
%o (PARI) Pi^4/384 \\ _Charles R Greathouse IV_, Oct 31 2014
%Y Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A260646.
%K nonn,cons
%O 0,1
%A _N. J. A. Sloane_, Feb 10 2013
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