A228881 - OEIS

%I #15 Mar 23 2021 15:47:39

%S 1,2,3,4,5,6,7,8,8,9,10,10,13,14,14,13,16,17,12,14,8,12,20,15,19,20,

%T 26,22,25,26,27,28,22

%N Minimum number of spheres touching a wall of the container in the densest packing of n equal spheres into a cube.

%C Spheres that are not part of the rigid framework, "rattlers", are always assumed not to touch the walls of the container cube.

%C If optimal configurations can be obtained by taking away an arbitrary sphere from a configuration with a higher sphere count, a sphere touching the container wall is chosen.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sphere/incube/spheresincube.html">Densest Packing of Spheres in a Cube</a> (Java Visualization)

%H Eckard Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html">The best known packings of equal spheres in a cube</a>, (complete up to N = 1000). [The title should be "The best packings known ..."! - _N. J. A. Sloane_, Mar 23 2021

%e The first configuration in which there is an inner sphere not touching the walls occurs for n = 9, with 8 spheres in the corners of the cube and one sphere in the center of the cube. Therefore a(9) = 8.

%Y Cf. A084824.

%K nonn,more

%O 1,2

%A _Hugo Pfoertner_, Sep 13 2013

%E a(25)-a(33) from _Hugo Pfoertner_, Mar 23 2021