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A192590 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 A192590 #4 Mar 30 2012 18:57:35
%S A192590 2,4,5,7,11,13,17,19,23,31,41,43,59,73,79,83,89,163,233,313,353,463,
%T A192590 929,1249,1409,4993
%N A192590 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 A192590 See the discussions at A192476 and A192580.
%t A192590 start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];
%t A192590 f[x_, y_] := If[MemberQ[primes, x*y - 3], x*y - 3]
%t A192590 b[x_] :=
%t A192590   Block[{w = x},
%t A192590    Select[Union[
%t A192590      Flatten[AppendTo[w,
%t A192590        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192590       200000 &]];
%t A192590 t = FixedPoint[b, start]    (* A192590 *)
%Y A192590 Cf. A192476, A192580.
%K A192590 nonn,fini,full
%O A192590 1,1
%A A192590 _Clark Kimberling_, Jul 05 2011