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A192649 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 1, 2, and 4 are in S.

%I A192649 #9 Sep 15 2018 08:53:37
%S A192649 1,2,3,4,5,7,8,9,12,15,16,17,21,24,31,32,33,39,40,45,48,55,56,60,63,
%T A192649 64,65,72,77,79,80,81,95,111,112,119,127,128,129,135,140,143,144,145,
%U A192649 152,159,161,175,176,185,192,200,207,208,209,216,221,223,224,225,231
%N A192649 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 1, 2, and 4 are in S.
%C A192649 See A192645.
%H A192649 Ivan Neretin, <a href="/A192649/b192649.txt">Table of n, a(n) for n = 1..10000</a>
%t A192649 start = {1, 2, 4};
%t A192649 f[x_, y_] := If[MemberQ[Range[1, 700], x^2 - y^2], x^2 - y^2]
%t A192649 b[x_] :=
%t A192649   Block[{w = x},
%t A192649    Select[Union[
%t A192649      Flatten[AppendTo[w,
%t A192649        Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t A192649       700 &]];
%t A192649 t = FixedPoint[b, start]  (* A192649 *)
%t A192649 Differences[t] (* A192650 *)
%Y A192649 Cf. A192476, A192646, A192650.
%K A192649 nonn
%O A192649 1,2
%A A192649 _Clark Kimberling_, Jul 06 2011