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A192614 Monotonic ordering of set S generated by these rules: if x and y are in S and 2x+y^2 is a prime, then 2x+y^2 is in S, and 1 is in S.

%I A192614 #4 Mar 30 2012 18:57:36
%S A192614 1,3,7,11,23,31,47,71,103,127,151,167,191,263,311,383,431,503,631,647,
%T A192614 743,863,887,911,967,983,1103,1151,1303,1487,1583,1607,1783,1823,1831,
%U A192614 1847,1871,2087,2207,2311,2351,2423,2447,2543,2591,2687,2927,3023
%N A192614 Monotonic ordering of set S generated by these rules:  if x and y are in S and 2x+y^2 is a prime, then 2x+y^2 is in S, and 1 is in S.
%C A192614 See the discussions at A192476 and A192580.
%t A192614 start = {1}; primes = Table[Prime[n], {n, 1, 1000}];
%t A192614 f[x_, y_] := If[MemberQ[primes, 2 x + y^2], 2 x + y^2]
%t A192614 b[x_] :=
%t A192614   Block[{w = x},
%t A192614    Select[Union[
%t A192614      Flatten[AppendTo[w,
%t A192614        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
%t A192614          Length[w]}]]]], # < 4000 &]];
%t A192614 t = FixedPoint[b, start]  (* A192614 *)
%t A192614 PrimePi[t]   (* A192615 *)
%Y A192614 Cf. A192476, A192580, A192615.
%K A192614 nonn
%O A192614 1,2
%A A192614 _Clark Kimberling_, Jul 05 2011