A133491 -id:A133491 - cp's OEIS frontend

A033177 Number of distinct distances between n electrons in minimal energy configuration on a sphere.

0, 1, 1, 1, 3, 2, 4, 4, 6, 7, 20, 3, 28, 9, 21, 12, 14, 18, 52, 26, 69, 17, 48, 16, 160, 168

Offset: 1

K. S. Brown (ksbrown(AT)seanet.com)

Most of the higher terms of this sequence just refer to the best configurations known today.

How is this defined if the optimal configuration is not unique? - N. J. A. Sloane, Feb 27 2009

			See Brown's web page in LINKS.

K. S. Brown, Min-Energy Configurations of Electrons On A Sphere, MathPages.
R. H. Hardin, N. J. A. Sloane & W. D. Smith, Table of best configurations presently known, Feb 1994.
Wikipedia, Thomson Problem.

Cf. A133491, A242617.

A133587 Conjectured order of the symmetry group of the (numerically computed) least-perimeter cluster of n nonoverlapping circles.

Original entry on oeis.org

4, 6, 4, 2, 10, 12, 14, 2, 4, 2, 6, 2, 4, 1, 2, 2, 2, 12, 2, 2, 1

Offset: 2

Keenan Pepper, Dec 27 2007

nonn

This can be thought of as the order of the symmetry group of the minimum-energy configuration of n two-dimensional bubbles in a plane. a(1) is infinite, because one bubble forms a circle, which has a continuous symmetry group containing rotations of arbitrary angles. So far, the actual symmetry groups are all dihedral, except for a(15) and a(22), which are trivial (their configurations have no symmetries).

			a(3) = 6 because three planar bubbles arrange themselves in an equilateral-triangle-type configuration with symmetry group D_3, of order 6.

Cox, S. J., F. Graner, M. F. Vaz, C. Monnereau-Pittet and N. Pittet, 2003, Minimal perimeter for N identical bubbles in two dimensions: calculations and simulations, Philos. Mag. 83, 1393-1406.
F. Morgan, Soap bubble clusters, Rev. Mod. Phys. Vol. 79 (2007), pp. 821-827.

R. L. Graham and N. J. A. Sloane, Penny-Packing and Two-Dimensional Codes, Discrete and Comput. Geom. 5 (1990), 1-11.

Cf. A133491.

cp's OEIS Frontend

A033177 Number of distinct distances between n electrons in minimal energy configuration on a sphere.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs