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%I #4 Mar 30 2012 18:57:36
%S 1,2,3,4,11,17,19,41,139,251,307,379,587,1699,3371
%N 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, 2, and 4 are in S.
%C See the discussions at A192476 and A192580.
%t start = {1, 2, 4}; primes = Table[Prime[n], {n, 1, 20000}];
%t f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 2 y^2]
%t b[x_] :=
%t Block[{w = x},
%t Select[Union[
%t Flatten[AppendTo[w,
%t Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
%t Length[w]}]]]], # < 30000 &]];
%t t = FixedPoint[b, start] (* A192613 *)
%Y Cf. A192612, A192476, A192580.
%K nonn,fini,full
%O 1,2
%A _Clark Kimberling_, Jul 05 2011
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