#!/usr/bin/env python
'''
Created on 21 oct. 2012

@author: Julien Lengrand-Lambert

DESCRIPTION: Solves problem 44 of Project Euler
Pentagonal numbers are generated by the formula, Pn=n(3n1)/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 is pentagonal
and D = |Pk - Pj| is minimised; what is the value of D?
'''
penta_vals = []


def is_pentagonal(val):
    """
    Returns True if val is a pentagonal number
    """
    global penta_vals
    return (val in penta_vals)


def pent(val):
    """
    Returns the pentagonal number created using val
    Pentagonal numbers are defined by Pn=n(3n-1)/2
    """
    return (val * (3 * val - 1) / 2)


def create_pentagonal(ite=1000):
    """
    Returns a list of ite pentagonal numbers
    default is 1000

    Pentagonal numbers are defined by Pn=n(3n1)/2
    """
    temp = range(1, ite + 1)
    return [pent(val) for val in temp]


def find_pair(ite=1000):
    """
    Finds the pair of pentagonal numbers such as
    Pj + Pk and Pj - Pk are also pentagonal
    Returns minimised |Pk - Pj|
    """
    global penta_vals

    penta_vals = create_pentagonal(ite)
    for val_j in penta_vals:
        for val_k in penta_vals:
            if is_pentagonal(val_k + val_j) and is_pentagonal(val_k - val_j):
                return min(abs(val_j - val_k), abs(val_k - val_j))

if __name__ == '__main__':
    print "Answer : %d " % (find_pair(10000))  # 10000 is just a rude guess