euler_030.py

# Euler 30
# Surprisingly there are only three numbers that can be written as the sum of fourth powers 
# of their digits:
#
# 1634 = 1^4 + 6^4 + 3^4 + 4^4
# 8208 = 8^4 + 2^4 + 0^4 + 8^4
# 9474 = 9^4 + 4^4 + 7^4 + 4^4
# As 1 = 1^4 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.

def sumOfDigitsToPower(number, power):
    return sum([int(x)**power for x in str(number)])

overallSum = 0
# I increased this times 10 at a time until it yielded no additional numbers
# I did not analyze why that is.
UPPER_LIMIT = 1000000
POWER = 5

for i in range(2,UPPER_LIMIT):
    if i == sumOfDigitsToPower(i,POWER):
        overallSum += i
        print(str(i) + " matches")

print(overallSum)