I don't think with regular integer bases, because integers can all be decomposed into primes, so you can create relations between different base representations

I don't think with regular integer bases, because integers can all be decomposed into primes, so you can create relations between different base representations, and if it's infinitely irregular in one, you can't wipe that out by converting it into another integer base....But maybe non-integer bases? Maybe base-phi? Or maybe some alternative to continued fractions? https://oeis.org/A001203 https://oeis.org/A001203