cp's OEIS Frontend

A154255 Floor of harmonic energy of the conjectural minimal-energy configurations of n points on the unit sphere in R^4, under the harmonic potential function.

%I A154255 #9 Sep 02 2024 19:36:25
%S A154255 0,1,2,4,6,9,13,17,22,28,34,41,49,57,66,76,87,98,110,123,137,152,167,
%T A154255 182,199,217,235,254,274,294,315,337,360,384,409,434,460,487,514,543,
%U A154255 572,601,632,664,697,730,764,799,835,871,909,947,985,1025,1066,1108
%N A154255 Floor of harmonic energy of the conjectural minimal-energy configurations of n points on the unit sphere in R^4, under the harmonic potential function.
%C A154255 Floor of the right-hand column of the subtable for k=4 given by Ballinger et al., in the table of data related to their paper. This table shows the conjectural minimal-energy configurations of n points on the unit sphere in R^k (for k from 2 to 64), under the harmonic potential function: the potential energy between two points at distance r is 1/r^(k-2). In each entry in the table, the column for n links to coordinates for the configuration (given as a plain text file in which each line lists the coordinates for one point).
%H A154255 B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, <a href="http://aimath.org/data/paper/BBCGKS2006/#4">This table shows the conjectural minimal-energy configurations of N points on the unit sphere in R^n...</a>
%H A154255 B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, <a href="https://arxiv.org/abs/math/0611451">Experimental study of energy-minimizing point configurations on spheres</a>, arXiv:math/0611451 [math.MG], 2006-2008.
%e A154255 a(7) = 9 because the harmonic energy given for 7 points on the 3-dimensional hypersurface of the 4-dimensional hypersphere is 9.500000000000 and floor(9.5) = 9. The coordinates of the 7 points are: (-0.774303376406259, -0.485591416628164, -0.399742015818543, +0.069725018266390); (-0.041986168871976, -0.225694667224730, +0.501037029764170, +0.834422539014180); (+0.041986168871976, +0.225694667224730, -0.501037029764170, -0.834422539014180); (+0.487341518427503, -0.842251530902810, +0.039549697743334, -0.227038376749526); (+0.104024891455872, +0.475037164815855, -0.683629522540632, +0.544214286758604); (+0.774303376406259, +0.485591416628164, +0.399742015818543, -0.069725018266390); (-0.591366409883375, +0.367214366086955, +0.644079824797298, -0.317175910009077).
%Y A154255 Cf. A153054.
%K A154255 nonn
%O A154255 2,3
%A A154255 _Jonathan Vos Post_, Jan 05 2009