Speedily calculate base 3 value of real huge integer number with Python 3

Question

We have a large number like (10**1500000)+1, and want to convert it to base 3. Below is running code with the fastest way we found with normal Python (without using numpy o

Answer 1

Here's a method that expands on your convsteps solution by recursing with the base squaring with each call. Some extra work is required to remove leading zeros.

def number_to_base(n, b):
    if n < b:
        return [n]
    else:
        digits = [d for x in number_to_base(n, b*b) for d in divmod(x, b)]
        return digits if digits[0] else digits[1:]

My quick timing test shows that it's the same as your step2 within the margin of error. But it's simpler and probably has fewer bugs.