Question 22
Let $\{a_k\}_{k=1}^{\infty}$ be an increasing sequence with $a_k\lt a_{k+1}$ for all $k=1,2,3,\ldots$ formed by arranging all the terms in the set $\{2^r+2^s+2^t:0\le r\lt s\lt t\}$ in increasing order. Find the largest value of the integer $n$ such that $a_n\le2020$.