Sequence generating idea

[David Wilson]

Here is an interesting way to (try to) generate integer sequences:

Let S be a set of integers.  Let S+n = {S+n : n in S}

Now peform the following algorithm

n = 0;
T = empty set;
a = empty sequence;
for (n = 0 to inf by 1) {
 if ( T intersect S+n = empty set ) {
  T = T union S+n;
  Append n to a;
 }
}

What is a if S = primes? squares? cubes? powers of 2? any other ideas?