TITLE: What sequence was I thinking of?
QUESTION [6 upvotes]: Ten years ago I blogged: 

I picked up my old, battered copy of
  G.H. Hardy's Pure Mathematics.  I haven't spent as much
  time reading this book as I should have; it's full of good stuff.
  There didn't seem to be anything in there about the Gaussian
  integers (digression: What's next in the sequence 1, 2, 4, 6, 10, 14,
  16, 24, 26?) but while scanning the index I noticed there was an entry
  for Ramanujan, so I checked it out.

What is next in the sequence 1, 2, 4, 6, 10, 14,
16, 24, 26? I can't remember.  Google search finds only this one mention from my blog.  OEIS doesn't know; the best I can do is A228898 which I'm sure is not what I had in mind.  There is probably something to it, and the answer will not be of the type "If you use Lagrange interpolation to fit the following 9th-degree polynomial… the next value is -163”, or the stops on the 7th avenue IRT train, or anything similarly obnoxious.
It must have something to do with Hardy's book, but I have no idea what.

REPLY [3 votes]: Daniel Fischer's comment is almost certainly the right answer:  

If 20 were in that sequence, I'd say the next number after 26 would be 36. Are you sure you didn't accidentally forget 20?

because these are positive integers $n$ such that $n+i$ is a gaussian prime.  Or, more simply, $n^2+1$ is prime. See OEIS A005574.
Perhaps I computed the values by hand and made a mistake on $20+i$.