What are Pentagonal Numbers?

A pentagonal number is a number that can be represented as the sum of five consecutive integers, starting from 1. The first few pentagonal numbers are:

1, 2, 5, 8, 12, 15, 19, 22, ... (sequence A006473 in the OEIS)

For example, the number 12 is a pentagonal number because it can be written as the sum of five consecutive integers:

1 + 2 + 3 + 4 + 5 = 12

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