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A192583 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, 4, 6, and 8 are in S.

%I A192583 #4 Mar 30 2012 18:57:35
%S A192583 2,4,5,6,8,11,13,17,23,31,37,41,47,53,67,79,83,89,103,107,137,139,149,
%T A192583 167,179,223,269,283,317,359,499,557,619,643,719,823,857,1097,1193,
%U A192583 1433,1439,1699,1997,2153,2477,2879,3343,4457,6857,7159,8599,12919,41143
%N A192583 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, 4, 6, and 8 are in S.
%C A192583 See the discussion at A192580.
%t A192583 start = {2, 4, 6, 8}; primes = Table[Prime[n], {n, 1, 10000}];
%t A192583 f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
%t A192583 b[x_] :=
%t A192583   Block[{w = x},
%t A192583    Select[Union[
%t A192583      Flatten[AppendTo[w,
%t A192583        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192583       10000000 &]];
%t A192583 t = FixedPoint[b, start]  (* A192583 *)
%t A192583 PrimePi[t] (* A192530 Nonprimes 4,6,8 are represented by "next prime down". *)
%Y A192583 Cf. A192476.
%K A192583 nonn,fini,full
%O A192583 1,1
%A A192583 _Clark Kimberling_, Jul 04 2011