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A084829
Best packing of m>1 equal spheres in a sphere setting a new density record.
5
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, 61
OFFSET
1,1
COMMENTS
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.
See the E. Specht link for latest results. - Eduard Baumann, Jan 03 2024
LINKS
WenQi Huang and Liang Yu, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, arXiv:1202.4149 [cs.DM], 2012.
Hugo Pfoertner, Densest Packings of n Equal Spheres in a Sphere of Radius 1 Largest Possible Radii.
Eric Weisstein's World of Mathematics, Sphere Packing.
Jianrong Zhou, Shuo Ren, Kun He, Yanli Liu, and Chu-Min Li, An Efficient Solution Space Exploring and Descent Method for Packing Equal Spheres in a Sphere, arXiv:2305.10023 [cs.CG], 2023.
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Hugo Pfoertner, Jun 12 2003
EXTENSIONS
Inserted missing term 30, added comment with conjectured next terms and updated links by Hugo Pfoertner, Jun 24 2011
More terms from Hugo Pfoertner, Aug 25 2013
STATUS
approved