A133587 - OEIS

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A133587

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

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

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OFFSET

2,1

COMMENTS

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).

REFERENCES

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.

LINKS

Table of n, a(n) for n=2..22.

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

EXAMPLE

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

CROSSREFS

Cf. A133491.

Sequence in context: A181774 A291379 A001138 * A204693 A204817 A199721

Adjacent sequences: A133584 A133585 A133586 * A133588 A133589 A133590

KEYWORD

nonn

AUTHOR

Keenan Pepper, Dec 27 2007

STATUS

approved