How to write 2**n - 1 as a recursive function?

I need a function that takes n and returns 2 n - 1 . It sounds simple enough, but the function has to be recursive. So far I have just 2n:

    def required_steps(n):
        if n == 0:
            return 1
        return 2 * req_steps(n-1)

The exercise states: "You can assume that the parameter n is always a positive integer and greater than 0"

2**n -1 is also 1+2+4+...+2 n-1 which can made into a single recursive function (without the second one to subtract 1 from the power of 2).

Hint : 1+2(1+2(...))

Solution below, don't look if you want to try the hint first.

This works if n is guaranteed to be greater than zero (as was actually promised in the problem statement):

    def required_steps(n):
        if n == 1: # changed because we need one less going down
            return 1
        return 1 + 2 * required_steps(n-1)

A more robust version would handle zero and negative values too:

    def required_steps(n):
        if n < 0:
            raise ValueError("n must be non-negative")
        if n == 0:
            return 0
        return 1 + 2 * required_steps(n-1)

(Adding a check for non-integers is left as an exercise.)

From: stackoverflow.com/q/58378549