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A084828 Maximum number of spheres of radius one that can be packed in a sphere of radius n. 5
1, 2, 13, 32, 68 (list; graph; refs; listen; history; text; internal format)
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.
Lower bounds for the next terms are a(6)>=122 and a(7)>=198. See E. Specht's webpage for latest data. - Hugo Pfoertner, Jan 22 2024
Sen Bai, X. Bai, X. Che, and X. Wei, Maximal Independent Sets in Heterogeneous Wireless Ad Hoc Networks, IEEE Transactions on Mobile Computing (Volume: 15, Issue: 8, Aug 01 2016), pp. 2023-2033.
Sunil K. Chebolu, Packing Moons Inside the Earth, arXiv:2006.00603 [physics.pop-ph], 2020.
WenQi Huang and Liang Yu, A Quasi Physical Method for the Equal Sphere Packing Problem, in 2011 IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications.
WenQi Huang and Liang Yu, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, arXiv preprint arXiv:1202.4149 [cs.DM], 2012. - From N. J. A. Sloane, Jun 14 2012
Cf. A121346 (conjectured lower bounds), A084827, A084829, A084825.
Cf. A023393 (2D).
Sequence in context: A285096 A177455 A185950 * A100512 A051474 A062708
Hugo Pfoertner, Jun 12 2003
Comment and links edited, a(5) from Hugo Pfoertner, Jun 23 2011
a(5) corrected, based on private communication from Yu Liang, by Hugo Pfoertner, Aug 24 2011

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