[seqfan] Largest subsets of {1, ..., n} such that no difference is ...

[Neil Sloane]

Dear Seqfans, A recent talk by Ben Green studies the density of, for
example, the largest subset of {1..n} such that no difference is:
(a) a square, (b) a prime - 1, (c) a prime, or (d) a prime + 1.

So let's look at the actual sizes, not the density.

I started off with (c), so let a(n) = max subset of {1..n} such that no
difference is a prime.  For n=1..11 I get
1,2,2,2,2,2,2,2,3,3,4
which seems not to be in the OEIS.
The examples where a(n) increases are {1}, {1,2}, {1,5,9}, {1,2,10,11}.
Could someone check?

And what about (a), (b), and (d)?

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com