Question 28
For $n\geq3$, the sequence of centred $n$-gon numbers is found by starting with a central dot, then adding layers consisting of $n$-gons of dots around this centre, where the number of dots on each side increases by 1 for each layer. For instance, the sequence of centred 7-gon numbers starts $1,8,22,43,\ldots$ as shown. What is the smallest $n$ for which 2017 is in the sequence of centred $n$-gon numbers?
