

A133491


Order of the symmetry group of the (in some cases conjectural) minimalenergy configuration of n identical charged particles confined to the surface of a sphere.


2



12, 24, 12, 48, 20, 16, 12, 16, 4, 120, 4
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OFFSET

3,1


COMMENTS

a(0), a(1) and a(2) are all infinite, because their symmetry groups are continuous (they contain rotations with arbitrary angles). Actual symmetry groups: 3 D_{3h}, 4 T_{d}, 5 D_{3h}, 6 O_{d}, 7 D_{5h}, 8 D_{4d}, 9 D_{3h}, 10 D_{4h}, 11 D_{1h}, 12 I_{d}, 13 D_{1h}.


LINKS

Table of n, a(n) for n=3..13.
K. S. Brown, MinEnergy Configurations of Electrons On A Sphere, MathPages.
R. H. Hardin, N. J. A. Sloane and W. D. Smith, Minimal Energy Configurations of Points on a Sphere
Wikipedia, Thomson Problem.


EXAMPLE

a(3)=12 because the minimalenergy configuration of 3 charged particles on a sphere is an equilateral triangle on the equator, which has symmetry group D_3h of order 12.


CROSSREFS

Cf. A033177, A242617.
Sequence in context: A072822 A239656 A059161 * A075606 A183192 A117320
Adjacent sequences: A133488 A133489 A133490 * A133492 A133493 A133494


KEYWORD

nonn,more


AUTHOR

Keenan Pepper, Nov 30 2007


STATUS

approved



