p044.py

#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 is pentagonal and D = |Pk - Pj| is minimised; what is the value of D?

import logging

def main(args):
    r = 5000

    Pentagonal = []
    for n in range(1,r):
        Pentagonal.append(n*(3*n-1)//2)

    sp = set(Pentagonal)
    d = Pentagonal[-1]

    for i in range(r-2):
        a = Pentagonal[i]
        for j in range(i+1, r-1):
            b = Pentagonal[j]
            if ((a+b in sp) and (b-a in sp)):
                logging.debug((a, b))
                if (d > b-a):
                    d = b-a
                    
    logging.info(d)