Euler problem #44

import math

di = {}  # Memoization


def cal_pentagonal(n):
    '''Calculate the pentagonal number'''
    if di.get(n):
        return di[n]
    else:
        result = (n * (3 * n - 1)) / 2
        di[n] = result
    return result


def is_pentagonal_number(x):
    n = (math.sqrt(x * 24 + 1) + 1) / 6
    return int(n) if n.is_integer() else False


def main():
    i = 1
    while True:
        i += 1
        l = cal_pentagonal(i)
        for k, v in di.items():
            if is_pentagonal_number(sum((l, v))) and is_pentagonal_number(abs(l - v)):
                return(i, k)


if __name__ == '__main__':
    main()
    # (2167, 1020)
    # CPU times: user 1.71 s, sys: 0 ns, total: 1.71 s
    # Wall time: 1.71 s
    # ==>> 5482660