IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 24

A sequence is defined by $a_{1}$=2, $a_{2}$=$2^{a_1}$, $a_{3}$=$2^{a_2}$, $a_{4}$=$2^{a_3}$, and so on. What is the least positive integer n for which $a_{n}$>10100?