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A084828
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Maximum number of spheres of radius one that can be packed in a sphere of radius n.
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5
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OFFSET
| 1,2
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COMMENTS
| a(4) and a(5) are experimental values. Although A121346(5) claims a lower bound of a(5)=68, it is conjectured from extensive numerical search that this value is unachievable and therefore a(5)=67.
The conjecture a(5)=67 was proved wrong by Yu Liang, who found an arrangement of 68 spheres of radius 1 fitting into a sphere of radius 5.
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LINKS
| Dave Boll, Optimal Packing of Circles and Spheres
Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
Hugo Pfoertner, Densest Packing of Spheres in a Sphere. Java visualization.
Yu Liang, Coordinates of sphere centers of 68 spheres of radius 0.20000222, fitting into a container of radius 1. Private communication, Aug 22, 2011
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CROSSREFS
| Cf. A121346 Conjectured lower bounds. A084827, A084829, A084825.
Sequence in context: A106959 A177455 A185950 * A100512 A051474 A062708
Adjacent sequences: A084825 A084826 A084827 * A084829 A084830 A084831
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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
| Comment and links edited, a(5) from Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 23 2011
a(5) corrected, based on private communication from Yu Liang, by Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 24 2011
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