Pentagon numbers

Pentagonal numbers are generated by the formula, \( P_n=\frac{n(3n−1)}{2} \). The first ten pentagonal numbers are:

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

It can be seen that \( P_4 + P_7 = 22 + 70 = 92 = P_8 \). However, their difference, \( 70 − 22 = 48 \), is not pentagonal.

Find the pair of pentagonal numbers, \( P_j \) and \( P_k \), for which their sum and difference are pentagonal and \( D = |P_k − P_j| \) is minimised; what is the value of \( D \)?