Hi,

I've been working on a project based upon the idea of 'stellar numbers'. That is, a number which, when represented as dots, can be arranged into the shape of a star withpvertices. This leads to a sequence for each value ofp, for example whenpis 6 (i.e. a six pointed star) the first five terms (S_{1}to S_{5}) would be:

1, 13, 37, 73, 121....and when is 3:

1, 7, 19, 37, 61...etc.

I worked out the first eight terms of the sequences for five values ofpand found a general statement:SThis obviously works for all terms I have actually found however I would like to know if there is a way that I can mathematically prove that this will work for any value of_{n }= pn^{2}- pn + 1

porn(providing they're natural numbers of course). Or is this unnecessary? Impossible?

Any help would be appreciated

Thanks,

jdbt