A084827 Maximum number of spheres of volume one that can be packed in a sphere of volume n.

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

Author

Hugo Pfoertner, Jun 09 2003

Keywords

• hard
• nonn

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).

Examples

			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.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..132
• Hugo Pfoertner, Densest packings of n equal spheres in a sphere of radius 1 (Table of largest possible radii)
• Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
• Eric Weisstein's World of Mathematics, World of Mathematics: Sphere Packing.

Crossrefs

Cf. A084828, A084829, A084824, A080865.

Extensions

More terms from Hugo Pfoertner, May 09 2005