Comment by Gro-Tsen on Is there an irrational number which in every base, has only 2 digits appear infinitely often?

@AnuragSahay One major difference is that the question you link to requires that every digit in base $3$ be in $\{0,2\}$ and every digit in base $4$ be in $\{0,3\}$ (and apparently there are even very few rationals satisfying this), whereas this question on bases $3$ and $4$ requires every digit after a certain point (so now it's much easier to find many rationals meeting the criterion).