Hamiltonian.2

[Colin Mallows]

And it seems that for each n there are only a finite number of solutions to 
Ham(x) = n.  For 0 <= n <= 20 the largest solutions under 100000  are

291,483,547,499,611,803,659,691,790,867,822,934,966,1123,1187,979,1110,1251,
1190,1315,1238.    

The number of solutions is remarkably stable: I find 

76,42,27,44,34,35,32,29,35,32,23,31,25,27,27,22,19,25,26,21,14.

   Colin Mallows (colinm at research.avayalabs.com)