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A192586 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2 and 4 are in S.

%I A192586 #6 Jul 14 2016 16:10:33
%S A192586 2,3,4,5,7,11,13,19,37,43,73
%N A192586 Monotonic ordering of set S generated by these rules:  if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2 and 4 are in S.
%C A192586 See the discussions at A192476 and A192580.
%t A192586 start = {2, 4}; primes = Table[Prime[n], {n, 1, 10000}];
%t A192586 f[x_, y_] := If[MemberQ[primes, x*y - 1], x*y - 1]
%t A192586 b[x_] :=
%t A192586   Block[{w = x},
%t A192586    Select[Union[
%t A192586      Flatten[AppendTo[w,
%t A192586        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192586       50000 &]];
%t A192586 t = FixedPoint[b, start]  (* A192586 *)
%Y A192586 Cf. A192476, A192580, A192587, A192588.
%K A192586 nonn,fini,full
%O A192586 1,1
%A A192586 _Clark Kimberling_, Jul 05 2011