125.py

"""Project Euler Problem 125: https://projecteuler.net/problem=125"""

# Recursively accumulates sums of consecutive squares and totals the palindromic values found.

is_palindrome = lambda n: str(n) == str(n)[::-1]

visited = set()


def recurse(start, num, total, limit):
    """Accumulate palindromic sums of consecutive squares starting at start."""

    if total >= limit:
        return 0

    if is_palindrome(total) and num - start > 0:
        if total not in visited:
            visited.add(total)

    return recurse(start, num + 1, total + (num + 1) * (num + 1), limit)


def solve(limit):
    """Sum all palindromic numbers below limit expressible as sums of consecutive squares."""
    for i in range(1, limit):
        recurse(i, i, i * i, limit)

    return sum(visited)


print(solve(10**8))