k-basis representation of natural numbers
Hint: For most infinite $S$, the languages $A_2(S),A_3(S)$ will both not be regular. Find some set $S$ for which $A_2(S)$ is regular (since the binary representations of numbers in $S$ are very simple), and with any luck $A_3(S)$ won't be regular. (Don't choose $S = \mathbb{N}$ or $S = \{ ax+b : x \in \mathbb{N} \}$.)