The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 62 + 72 + 82 + 92 + 102 + 112 + 122.
There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 02 + 12 has not been included as this problem is concerned with the squares of positive integers.
Find the sum of all the numbers less than 108 that are both palindromic and can be written as the sum of consecutive squares.
To solve this problem requires a simple search to the square root of the limit (108) or 5,000. We use a set to eliminate duplicate sum-of-squares.
Runs < 1 second in Python.
from Euler import is_palindromic limit = 10**8 sqrt_limit = int(limit**.5) pal = set() for i in range(1, sqrt_limit): sos = i*i for j in range(i+1, sqrt_limit): sos += j*j if sos>=limit: break if is_palindromic(sos): pal.add(sos) print "Answer to PE125 = ", sum(pal), len(pal)
- More information on the Euler module can be found on the tools page.
- Takes 371,234 iterations.
- The second number printed is the size of the set.