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A192592 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+2y is a prime, then 3x+2y is in S, and 1 is in S.

%I A192592 #8 May 08 2017 09:22:52
%S A192592 1,5,13,17,29,37,41,53,61,73,89,97,109,113,137,149,157,173,181,193,
%T A192592 197,229,233,241,257,269,277,281,293,313,317,337,349,353,373,389,397,
%U A192592 401,409,421,433,449,457,461,509,521,541,557,569,577,593,601,613,617
%N A192592 Monotonic ordering of set S generated by these rules:  if x and y are in S and 3x+2y is a prime, then 3x+2y is in S, and 1 is in S.
%C A192592 See the discussions at A192476 and A192580.
%H A192592 Vincenzo Librandi, <a href="/A192592/b192592.txt">Table of n, a(n) for n = 1..609</a>
%t A192592 start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
%t A192592 f[x_, y_] := If[MemberQ[primes, 2 x + 3 y], 2 x + 3 y]
%t A192592 b[x_] :=
%t A192592   Block[{w = x},
%t A192592    Select[Union[
%t A192592      Flatten[AppendTo[w,
%t A192592        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
%t A192592          Length[w]}]]]], # < 1000 &]];
%t A192592 t = FixedPoint[b, start]     (* A192592 *)
%t A192592 PrimePi[t]    (* A192593 *)
%Y A192592 Cf. A192476, A192580, A192593.
%K A192592 nonn
%O A192592 1,2
%A A192592 _Clark Kimberling_, Jul 05 2011