

A084828


Maximum number of spheres of radius one that can be packed in a sphere of radius n.


5




OFFSET

1,2


COMMENTS

a(4) and a(5) are experimental values. Although A121346(5) claims a lower bound of a(5)=68, it is conjectured from extensive numerical search that this value is unachievable and therefore a(5)=67.
The conjecture a(5)=67 was proved wrong by Yu Liang, who found an arrangement of 68 spheres of radius 1 fitting into a sphere of radius 5.
Lower bounds for the next terms are a(6)>=122 and a(7)>=198. See E. Specht's webpage for latest data.  Hugo Pfoertner, Jan 22 2024


LINKS



CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS

a(5) corrected, based on private communication from Yu Liang, by Hugo Pfoertner, Aug 24 2011


STATUS

approved



