Palindromic Binary Numbers

We call a non-negative number $x$ good if its binary representation is palindromic. For example, $107$ is good because its binary representation is $1101011$ which is palindromic while $10$ is not good because its binary representation is $1010$ which is not palindromic. Recall that, a string is said to be palindromic if it reads the same backward as forward. You are given a number $n$. You have