Question 81
Determine whether there exists an infinite sequence of integers $a_1, a_2, a_3, \dots$ with $0 \lt a_i \lt 10$ and a positive integer $N$ such that, for every integer $k \gt N$, the number
$$
\sum_{i=1}^{k} a_i 10^{i-1}
$$
is a perfect square?
$$
\sum_{i=1}^{k} a_i 10^{i-1}
$$
is a perfect square?