Quibbles

1. Why isn't (as implied by the totality of your post) your your initial value, 112358, "a bona fide integer?"
2. "the fact that a number is divisible by 3 if the sum of digits of that number is divisible by 3."
     Sounds good but for us non-mathematicians, please cite an authoritative source.
3. Using Base3 numbers on a quantum computer will break your algorithm.
               :-)

Seriously, very nice. ++ for "well done."