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A192596 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.

%I A192596 #4 Mar 30 2012 18:57:36
%S A192596 1,7,31,97,127,409,601,769,1231,1657,1831,2017,2311,3079,3169,3457,
%T A192596 3631,3697,3943,4201,4999,5479,5521,5881,6079,6151,6607,6961,7057,
%U A192596 7129,7321,7417,7687,8089,8161,8431,9127,9241,9337,9511,9631,9871,10009
%N A192596 Monotonic ordering of set S generated by these rules:  if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.
%C A192596 See the discussions at A192476 and A192580.
%t A192596 start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
%t A192596 f[x_, y_] := If[MemberQ[primes, 3 x + 4 y], 3 x + 4 y]
%t A192596 b[x_] :=
%t A192596   Block[{w = x},
%t A192596    Select[Union[
%t A192596      Flatten[AppendTo[w,
%t A192596        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
%t A192596          Length[w]}]]]], # < 20000 &]];
%t A192596 t = FixedPoint[b, start]    (* A192596 *)
%t A192596 PrimePi[t]   (* A192597 *)
%Y A192596 Cf. A192574, A192580, A192597.
%K A192596 nonn
%O A192596 1,2
%A A192596 _Clark Kimberling_, Jul 05 2011