MathNet 2016-part-07 — 182 problems (EN–VI) Question 69

Let the sequence $a_{i}$ be defined as $a_{i+1} = 2^{a_{i}}$. Find the number of integers $1 \leq n \leq 1000$ such that if $a_{0} = n$, then $100$ divides $a_{1000} - a_{1}$.