Tavas has a peculiar habit of eating coffee mix without water, despite the unpleasant smell. Keione, his friend, decided to teach him a lesson and enlisted the help of SaDDas. SaDDas took Tavas' headphones and challenged him to solve a problem in order to get them back. The problem is as follows: Given a lucky number n, where lucky numbers are positive integers that only contain the digits 4 and 7 in their decimal representation, determine the 1-based index of n when all lucky numbers are sorted in increasing order. Since Tavas is not as skilled as SaDDas, he seeks your assistance in solving this problem and retrieving his headphones.