A227416 Magic numbers from Smale’s 7th problem.

6, 12, 24, 32, 48, 60, 67, 72, 80, 104, 108, 122, 132, 137

Offset

1,1

Comments

See pp. 16-17 of Nerattini et al. The sequence is defined as the numbers n of points distributed on the two-sphere in such a way that their average logarithmic pair-energy 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 [math-ph], August 08, 2013.

S. Smale,  Mathematical problems for the next century, Math. Intelligencer 20 (1998), pp 7-15.

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