Question 58
Felix chooses a positive integer as the starting number and writes it on the board. He then repeats the next step: he replaces the number $n$ on the board by $\frac{1}{2}n$ if $n$ is even and by $n^2 + 3$ if $n$ is odd. For how many choices of starting numbers below 2023 will Felix never write a number of more than four digits on the board?