A126195 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.

12, 28, 52, 83, 120

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..5.

D. Eppstein, Sphere Packing and Kissing numbers.

J. Fliege, Integration nodes for the sphere.

N. J. A. Sloane, Spherical codes.

Crossrefs

Sequence in context: A223454 A107707 A183053 * A248547 A164533 A034319

Adjacent sequences: A126192 A126193 A126194 * A126196 A126197 A126198

Keyword

more,nonn

Author

R. J. Mathar, Mar 07 2007, corrected Apr 03 2007

Extensions

Updated Fliege's URL - R. J. Mathar, Feb 05 2010

Status

approved