This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242088 #17 Feb 16 2025 08:33:22 %S A242088 0,0,1,3,6,9,12 %N A242088 Number of edges in the convex hull of a rigorous solution to Thomson's problem for n points. %C A242088 Thomson’s problem is to determine the stable equilibrium configuration(s) of n particles confined to the surface of a sphere and repelling each other by an inverse square force. %C A242088 Rigorous solutions are known only for n <= 6 and n = 12, with a(12) = 30. %C A242088 Non-rigorous solutions are given in Wikipedia for all n <= 460. The least non-monotonic pair is 63 > 60 for n = 23 and 24, respectively. %H A242088 Kevin Brown, <a href="http://mathpages.com/home/kmath005/kmath005.htm">Min-Energy Configurations of Electrons On A Sphere</a> %H A242088 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ThomsonProblem.html">Thomson Problem</a> %H A242088 Wikipedia, <a href="https://en.wikipedia.org/wiki/Thomson_problem">Thomson problem</a> %F A242088 a(n) <= n(n-1)/2 = (n choose 2). %F A242088 a(n) <= 3*n-6 = A008585(n-2) for n >= 3, since a solution to Thomson's problem gives a planar graph, which has 3*n-6 edges if it is maximal (see A008486 comments). - _Jonathan Sondow_, Mar 03 2018 answering a question by Joseph Wheat. %e A242088 For n = 0 or 1 points, the convex hull is empty or a point, so there are no edges and a(0) = a(1) = 0. %Y A242088 Cf. A008486, A008585, A080865, A242617, A268487. %K A242088 more,hard,nonn %O A242088 0,4 %A A242088 _Jonathan Sondow_, May 04 2014