Nguyen writes down some numbers according to the following rules. Starting with the number $1$, he doubles the number and adds $4$, so the second number he writes is $6$. He now repeats this process, starting with the last number written doubling and then adding $4$, but he doesn\textquotesingle t write the hundreds digit if the number is bigger than $100$. What is the $2022^{}\text{nd}$ number that Nguyen writes down? (2022AMC 29) 
Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences