

A307983


Consider a pentagonal bipyramid with its seven vertices P_1, ..., P_7 lying on a unit sphere; sequence gives decimal expansion of Sum_{i < j} 1/dist(P_i, P_j).


0



1, 4, 4, 5, 2, 9, 7, 7, 4, 1, 4, 2, 2, 1, 3, 4, 2, 9, 3, 5, 0, 4, 4, 4, 9, 1, 5, 3, 0, 6, 0, 2, 9, 2, 8, 7, 9, 0, 4, 7, 7, 8, 5, 6, 0, 5, 6, 9, 2, 5, 5, 3, 3, 6, 8, 2, 7, 1, 1, 7, 7, 7, 5, 1, 8, 0, 4, 9, 1, 3, 8, 3, 6
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OFFSET

2,2


COMMENTS

The seven points are the vertices of a regular pentagon inscribed in the equator plus the North and South poles.
Conjecturally, this is the solution to the Thompson problem with 7 electrons: given 7 points on the surface of a unit sphere, minimize the sum of the inverse distances between pairs of points. (This models electrostatic potential energy in the plum pudding model of the atom. N = 7 electrons is the first unresolved case.)
An octic number with denominator 2 and minimal polynomial 256x^8  1024x^7  75008x^6 + 228608x^5 + 5537120x^4  11456448x^3  103335888x^2 + 109102384x  23637199.


LINKS

Table of n, a(n) for n=2..74.
Kevin S. Brown, MinEnergy Configurations of Electrons On A Sphere
Wikipedia, Thompson problem


FORMULA

1/2 + 10/sqrt(2) + 5/sqrt((5+sqrt(5))/2) + 5/sqrt((5sqrt(5))/2) = 1/2 + 5*sqrt(2)*(1 + sqrt(1/2 + 1/sqrt(5))).


EXAMPLE

14.452977414221342935044491530602928790477856056925533682711777518049....


CROSSREFS

Sequence in context: A019922 A092171 A179778 * A011333 A283268 A016709
Adjacent sequences: A307980 A307981 A307982 * A307984 A307985 A307986


KEYWORD

nonn,cons


AUTHOR

Charles R Greathouse IV, May 09 2019


STATUS

approved



