000=1, 001=2, 002=3, 010=4, 011=5, 012=6, 020=7, 022=8, 100=9, 101...

Don't care much for your starting point there, moose. How about:
000=0, 001=1, 002=2, 010=3, 011=4, 012=5, 020=6, 021=7, 022=8, 100...

Trinary sounds good, though.