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Search: id:A133491
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| A133491 |
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Order of the symmetry group of the (in some cases conjectural) minimal-energy configuration of n identical charged particles confined to the surface of a sphere. |
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+0
2
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| 12, 24, 12, 48, 20, 16, 12, 16, 4, 120, 4
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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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}.
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LINKS
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R. H. Hardin, N. J. A. Sloane and W. D. Smith, Minimal Energy Configurations of Points on a Sphere
MathPages, Min-Energy Configurations of Electrons On A Sphere
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EXAMPLE
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a(3)=12 because the minimal-energy configuration of 3 charged particles on a sphere is an equilateral triangle on the equator, which has symmetry group D_3h of order 12.
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CROSSREFS
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Sequence in context: A015447 A072822 A059161 this_sequence A075606 A117320 A040132
Adjacent sequences: A133488 A133489 A133490 this_sequence A133492 A133493 A133494
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KEYWORD
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nonn
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AUTHOR
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Keenan Pepper (keenanpepper(AT)gmail.com), Nov 30 2007
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