cp's OEIS Frontend

A084829 Best packing of m>1 equal spheres in a sphere setting a new density record.

%I A084829 #45 Feb 16 2025 08:32:49
%S A084829 2,3,4,6,8,9,11,12,18,21,25,30,31,32,33,34,35,36,38,49,51,53,56,59,60,
%T A084829 61
%N A084829 Best packing of m>1 equal spheres in a sphere setting a new density record.
%C A084829 All terms beyond m=9 are only conjectures found by numerical experimentation. The density is defined as the fraction of the volume of the large sphere occupied by the small spheres. For 2 spheres the density is 0.25. The first known configuration with density exceeding 0.5 occurs for 31 spheres.
%C A084829 See the E. Specht link for latest results. - _Eduard Baumann_, Jan 03 2024
%H A084829 Dave Boll, <a href="http://web.archive.org/web/20121213221349/https://home.comcast.net/~davejanelle/packing.html">Optimal Packing of Circles and Spheres</a>.
%H A084829 WenQi Huang and Liang Yu, <a href="http://arxiv.org/abs/1202.4149">Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem</a>, arXiv:1202.4149 [cs.DM], 2012.
%H A084829 Eckard Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/ssp/ssp.html">The best known packings of equal spheres in a sphere</a>, July 2023.
%H A084829 Hugo Pfoertner, <a href="/A084827/a084827.txt">Numerical results for best packing of spheres in sphere</a>.
%H A084829 Hugo Pfoertner, <a href="/A084829/a084829.txt">Densest Packings of n Equal Spheres in a Sphere of Radius 1</a> Largest Possible Radii.
%H A084829 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SpherePacking.html">Sphere Packing</a>.
%H A084829 Jianrong Zhou, Shuo Ren, Kun He, Yanli Liu, and Chu-Min Li, <a href="https://arxiv.org/abs/2305.10023">An Efficient Solution Space Exploring and Descent Method for Packing Equal Spheres in a Sphere</a>, arXiv:2305.10023 [cs.CG], 2023.
%Y A084829 Cf. A084827, A084826, A084644, A084828, A121346.
%K A084829 hard,more,nonn
%O A084829 1,1
%A A084829 _Hugo Pfoertner_, Jun 12 2003
%E A084829 Inserted missing term 30, added comment with conjectured next terms and updated links by _Hugo Pfoertner_, Jun 24 2011
%E A084829 More terms from _Hugo Pfoertner_, Aug 25 2013