Quick Problem: Is there an efficient way to do operations on an integer number $ n $ so that it can be written as $ 2 ^ N – 1 $

For example 7 can be written as
$$
7 cdot (9) = 2 ^ 6 – 1
$$

However, any unitary or binary operation can be used as long as there is an efficient way to get there. I've never seen anything like this before and it just came to a more general problem that I solve.