# nt.number theory – Frequency of digits in powers of \$ 2, 3, 5 \$ and \$ 7 \$

For a fixed integer $$N in mathbb {N}$$ consider the multi-set $$A_2 (N)$$ of decimal digits of $$2 ^ n$$, for $$n = 1,2, points, N$$. For example,
$$A_2 (8) = {2,4,8,1,6,3,2,6,4,1,2,8,2,5,6 }.$$
Similarly, define multiple sets. $$A_3 (N), A_5 (N)$$ Y $$A_7 (N)$$.

I can not be sure of having seen any discussion about the next question. If you do, please let me know of a reference.

QUESTION. by $$N$$ large, is it true that the most frequent digit in $$A_x (N)$$ is $$x$$, where $$x in {2,3,5,7 }$$?