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A192612 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 and 2 are in S.

%I A192612 #5 Mar 30 2012 18:57:36
%S A192612 1,2,3,11,17,19,139,251,307,379,587
%N A192612 Monotonic ordering of set S generated by these rules:  if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 and 2 are in S.
%C A192612 See the discussions at A192476 and A192580.  The start-set for A192612 is {1,2}.  For results using start-sets {1}, and {1,2,4}, see A192598 and A192613.
%t A192612 start = {1, 2}; primes = Table[Prime[n], {n, 1, 20000}];
%t A192612 f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 2 y^2]
%t A192612 b[x_] :=
%t A192612   Block[{w = x},
%t A192612    Select[Union[
%t A192612      Flatten[AppendTo[w,
%t A192612        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
%t A192612          Length[w]}]]]], # < 30000 &]];
%t A192612 t = FixedPoint[b, start]  (* A192612 *)
%Y A192612 Cf. A192476, A192580, A192613.
%K A192612 nonn,full,fini
%O A192612 1,2
%A A192612 _Clark Kimberling_, Jul 05 2011