

A227416


Magic numbers from Smale’s 7th problem.


0



6, 12, 24, 32, 48, 60, 67, 72, 80, 104, 108, 122, 132, 137
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

See pp. 1617 of Nerattini et al. The sequence is defined as the numbers n of points distributed on the twosphere in such a way that their average logarithmic pairenergy is minimal, and locally convex as a function of n. So far the available data for this sequence are empirical and should eventually be vindicated, or replaced if necessary, by rigorous data. The name "magic numbers" alludes to a similarity with the "magic numbers" in nuclear physics, see A018226.


LINKS

Table of n, a(n) for n=1..14.
Rachele Nerattini, Johann S. Brauchart, Michael K.H. Kiessling, Magic numbers in Smale's 7th problem, arXiv:1307.2834v2 [mathph], August 08, 2013.
S. Smale, Mathematical problems for the next century, Math. Intelligencer 20 (1998), pp 715.


CROSSREFS

Cf. A018226.
Sequence in context: A110967 A000082 A263849 * A106697 A323002 A249127
Adjacent sequences: A227413 A227414 A227415 * A227417 A227418 A227419


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Jul 10 2013


EXTENSIONS

Comment section and reference section corrected and revised by Michael Kiessling, Aug 20 2013


STATUS

approved



