'''
Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?
'''

import math

def p(n):
    return int(n * (3 * n - 1) / 2)

def isTriangle(n, triangleSet, triangleList):
    if n > triangleList[-1]:
        toBeat = triangleList[-1]
        m = len(triangleList)

        while toBeat < n:
            m += 1
            toBeat = p(m)
            triangleList.append(toBeat)
            triangleSet.add(toBeat)
        
        return n == triangleList[-1]

    else:
        return n in triangleSet

def main():
    print("Hello this is Patrick")

    bestDif = math.inf
    triangleList = [1, 5]
    triangleSet = set(triangleList)

    for i in range(2, 10000):
        for j in range(1, i):
            if isTriangle(p(i) - p(j), triangleSet, triangleList) and isTriangle(p(i) + p(j), triangleSet, triangleList):
                bestDif = min(bestDif, abs(p(i) - p(j)))

    print(bestDif)


if __name__ == "__main__":
    main()