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A268487 Numbers of equal electric charges for which the minimum-potential dislocation on a sphere has nonzero sum of position vectors. 1
11, 13, 19, 21, 25, 26, 31, 33, 35, 43, 47, 49, 52, 53, 54, 55, 59, 61, 65, 66, 71, 73, 74, 76, 79, 81, 83, 84, 85, 86, 87, 89, 91, 93, 95, 96, 97, 98, 99, 103, 107, 108, 109, 114, 115, 116, 117, 118, 119, 120, 121, 123, 125, 128, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Probably most of these terms are merely conjectural. - N. J. A. Sloane, Mar 31 2016

Given m identical point charges located on a sphere, their minimum-potential dislocation (the Thomson problem) may, but need not, have high enough symmetry for the sum of their position vectors Sum[i=1..m](r_i) to be zero. This sequence lists, in increasing order, the values of m for which the sum is nonzero.

Numeric investigations were carried out by various authors for m = 1 to 204, and then for a number of selected cases (see references in the Wikipedia link). Among the studied cases, 312 is also known to belong to this sequence. All these cases have at most some type of C-symmetry (C_2,C_2v,C_s,C_3,C_3v). So far, 10 cases with no symmetry at all (C_1) were found, namely m = 61, 140, 149, 176, 179, 183, 186, 191, 194, 199. No simple algorithm to handle this open problem, nor a general formula, are known.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..100

Steve Smale, Mathematical Problems for the Next Century, Mathematical Intelligencer, 20 (1998), 7-15.

Wikipedia, Thomson problem

CROSSREFS

Sequence in context: A090137 A205707 A136491 * A216687 A005360 A269806

Adjacent sequences:  A268484 A268485 A268486 * A268488 A268489 A268490

KEYWORD

nonn,hard

AUTHOR

Stanislav Sykora, Feb 08 2016

STATUS

approved

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Last modified June 23 18:12 EDT 2017. Contains 288668 sequences.