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A084829
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Best packing of m>1 equal spheres in a sphere setting a new density record.
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3
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2, 3, 4, 6, 8, 9, 11, 12, 18, 21, 25, 30, 31, 32
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
Conjectured next terms: 33, 34, 35, 36, 38, 49.
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LINKS
| Dave Boll, Optimal Packing of Circles and Spheres
Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
Eric Weisstein's World of Mathematics, World of Mathematics: Sphere Packing.
Hugo Pfoertner, Densest Packings of n Equal Spheres in a Sphere of Radius 1. Largest Possible Radii
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CROSSREFS
| Cf. A084827, A084826, A084644, A084828.
Sequence in context: A020900 A002479 A010458 * A018649 A135676 A102701
Adjacent sequences: A084826 A084827 A084828 * A084830 A084831 A084832
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KEYWORD
| hard,more,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 12 2003
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EXTENSIONS
| Inserted missing term 30, added comment with conjectured next terms and updated links by Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 24 2011
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