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A192589 Monotonic ordering of set S generated by these rules: if x and y are in S and xy+3 is a prime, then xy+3 is in S, and 2 and 4 are in S.

%I A192589 #6 Jan 03 2014 15:57:39
%S A192589 2,4,7,11,17,19,31,37,41,47,71,79,97,127,151,167,191,197,257,337,397,
%T A192589 607,677,797,1031,1217,1597,2437,2711,3191,4127,4871,4877,10847,43391
%N A192589 Monotonic ordering of set S generated by these rules:  if x and y are in S and xy+3 is a prime, then xy+3 is in S, and 2 and 4 are in S.
%C A192589 See the discussions at A192476 and A192580.
%t A192589 start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];
%t A192589 f[x_, y_] := If[MemberQ[primes, x*y + 3], x*y + 3]
%t A192589 b[x_] :=
%t A192589   Block[{w = x},
%t A192589    Select[Union[
%t A192589      Flatten[AppendTo[w,
%t A192589        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192589       200000 &]];
%t A192589 t = FixedPoint[b, start]    (* A192589 *)
%Y A192589 Cf. A192476 and A192580.
%K A192589 nonn,fini,full
%O A192589 1,1
%A A192589 _Clark Kimberling_, Jul 05 2011