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A084827
Maximum number of spheres of volume one that can be packed in a sphere of volume n.
5
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 38, 38, 38, 38, 39, 39, 40, 40, 42, 42, 42, 43, 43, 44
OFFSET
1,8
COMMENTS
Higher terms of the sequence are only conjectures derived from numerical results. The first 12 arrangements are identical with the solutions of the Tammes problem (see A080865).
LINKS
Hugo Pfoertner, Densest packings of n equal spheres in a sphere of radius 1 (Table of largest possible radii)
Eric Weisstein's World of Mathematics, World of Mathematics: Sphere Packing.
EXAMPLE
a(10)=2 because a sphere of volume 10 is slightly too small to cover 3 mutually touching spheres of volume 1. a(27)=13 because the arrangement of 12 spheres plus one central sphere needs exactly a sphere with R=3*r to be contained.
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Hugo Pfoertner, Jun 09 2003
EXTENSIONS
More terms from Hugo Pfoertner, May 09 2005
STATUS
approved