Three Tri-Automorphic Numbers for each Number of Digits

Theorem
Let $d \in \Z_{>0}$ be a (strictly) positive integer.

Then there exist exactly $3$ tri-automorphic numbers with exactly $d$ digits.

These tri-automorphic numbers all end in $2$, $5$ or $7$.

Proof
Let $n$ be a tri-automorphic number with $d$ digits.