%I #5 Oct 04 2012 10:28:58
%S 12,28,52,83,120
%N Conjectured values for maximal number of solid spheres of radius 1 that can be rolled all in touch with and on the outside surface of a sphere of radius n.
%C A solid sphere of unit radius in touch with and outside a sphere of radius n occupies a projected angle of theta=2*arcsin[1/(1+n)]. (In the projection, the large sphere center, the small sphere center and the point where the tangent from the large sphere center touches the small sphere form a rectilinear triangle with hypotenuse of length 1+n and one cathetus of length 1. One of the angles in the triangle is theta/2.) Values have been obtained by reverse interpolation of these angles theta(n=1,2,3,...)=60, 38.9, 28.95,... degrees etc. from the "min separation" column of the Sloane table to the "npts" column, rounding npts down.
%H D. Eppstein, <a href="http://www.ics.uci.edu/~eppstein/junkyard/spherepack.html">Sphere Packing and Kissing numbers</a>.
%H J. Fliege, <a href="http://www.personal.soton.ac.uk/jf1w07/nodes/nodes.html">Integration nodes for the sphere</a>.
%H N. J. A. Sloane, <a href="http://neilsloane.com/packings/">Spherical codes</a>.
%K more,nonn
%O 1,1
%A _R. J. Mathar_, Mar 07 2007, corrected Apr 03 2007
%E Updated Fliege's URL - _R. J. Mathar_, Feb 05 2010