euler030.py

#!/usr/bin/env python
"""
Solution to Project Euler Problem 30
http://projecteuler.net/

by Apalala <apalala@gmail.com>
(cc) Attribution-ShareAlike
http://creativecommons.org/licenses/by-sa/3.0/


Surprisingly there are only three numbers that can be written as the sum of
fourth powers of their digits:

    1634 = 14 + 64 + 34 + 44
    8208 = 84 + 24 + 04 + 84
    9474 = 94 + 44 + 74 + 44

As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers
of their digits.
"""
from itertools import count
from digits import digits


def power_of_digits(n, k):
    return (x ** k for x in digits(n))


def numbers_that_sum_power_of_digits(k):
    for n in count(2):
        d = list(digits(n))
        if len(d) * (9 ** k) < n:
            break
        if n == sum(power_of_digits(n, k)):
            yield n


def test():
    assert 19316 == sum(numbers_that_sum_power_of_digits(4))


def run():
    print(sum(numbers_that_sum_power_of_digits(5)))


if __name__ == "__main__":
    test()
    run()