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A192648 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2-y^2>0 then x^2-y^2 is in S, and 2 and 3 are in S.

%I A192648 #8 Sep 15 2018 08:52:41
%S A192648 2,3,5,16,21,185,231,247,252,416,432,437,2495,4345,7648,10143,13568,
%T A192648 17913,19136,26784,29279,33784,33969,34200,34216,34221,52920,53105,
%U A192648 53336,53352,53357,60568,60753,60984,61000,61005,63063,63248,63479
%N A192648 Monotonic ordering of set S generated by these rules:  if x and y are in S and x^2-y^2>0 then x^2-y^2 is in S, and 2 and 3 are in S.
%C A192648 See A192645.
%H A192648 Ivan Neretin, <a href="/A192648/b192648.txt">Table of n, a(n) for n = 1..10000</a>
%t A192648 start = {2, 3};
%t A192648 f[x_, y_] := If[MemberQ[Range[1, 150000], x^2 - y^2], x^2 - y^2]
%t A192648 b[x_] :=
%t A192648   Block[{w = x},
%t A192648    Select[Union[
%t A192648      Flatten[AppendTo[w,
%t A192648        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192648       150000 &]];
%t A192648 t = FixedPoint[b, start]  (* A192648 *)
%Y A192648 Cf. A192476, A192646.
%K A192648 nonn
%O A192648 1,1
%A A192648 _Clark Kimberling_, Jul 06 2011