Project Euler, Problem 44: Pentagon Numbers

Pentagonal numbers are generated by the formula, $P_{n} = \frac{3 n^{2} - n}{2}$ . 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

Runtime: 0

Average: 0 Runs: 0

SD: 0 ms

Max: 0

Min: 1000

To start I made an array of pentagonal numbers to work with. From there I found the differences between progressively further apart numbers. When I found a difference that was also a pentagonal number I checked if sum of the subtrahend and minuend was also pentagonal.

Out of the 10,000 pentagonal numbers I generated, I only found one match.

58,974