Hmm I think maybe it's worth being more precise on what we mean by functions now. I guess probably a good way of saying this is that functions are elements of $\mathcal{O}(U)$ for some open set $U$, where $\mathcal{O}$ is your structure sheaf.

So in this sense it doesn't quite make sense to ask for functions defined at the generic point - but maybe you want to know what are the functions that are defined on any open set containing the generic point - here's the catch - every open set on an irreducible space contains the generic point.

So I have a sequence that smells funky, and I'm not sure what sort of thing is producing it. I feel like it's weird enough that it's probably something someone's seen.

For each prime number p >= 5 (currently looked up to about 100), there is a number n = p-1 or p+1 such that each entry whose index is divisible by n is also divisible by p.

For example, N_6, N_12, N_18, etc... all have exactly one 5 as a prime factor.
But N_10, N_20, N_30, etc... all have exactly one 11 as a prime factor

But as it turns out, N_3, N_9, etc, also have a factor of 5 too. Sometimes it's not just N_{n*i} for i …