There are definitely properties of numbers that are more easily stated in one base vs. another, but I don't see how an automata would matter. Any automata that

There are definitely properties of numbers that are more easily stated in one base vs. another, but I don't see how an automata would matter. Any automata that can process strings in one base can be converted into an automata that can process strings in any other base. An example of such a property is that a real number in the interval [0,1] is a member of the Cantor set if and only if it has no 1's in its base 3 representation (not a typo, yes, base 3).