Programming puzzle: Longest list of regular numbers?

[Dave Britten]

Tip: These are just the "Hamming numbers".

A quick-and-dirty TI-86 program for a simplistic algorithm got me H(395)=295,245.

A similar program for my Casio fx-9860g Slim failed at about 24 seconds, as it had already found 999 and hit the maximum length of a list. Would have to work around this by garbage collecting unneeded entries from the beginning of the list to keep it short.