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.

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, 64, 65, 72, 77, 79, 80, 81, 95, 111, 112, 119, 127, 128, 129, 135, 140, 143, 144, 145, 152, 159, 161, 175, 176, 185, 192, 200, 207, 208, 209, 216, 221, 223, 224, 225, 231

Offset: 1

Author

Clark Kimberling, Jul 06 2011

Keywords

• nonn

Comments

See A192645.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A192476, A192646, A192650.

Programs

Mathematica

start = {1, 2, 4};
f[x_, y_] := If[MemberQ[Range[1, 700], x^2 - y^2], x^2 - y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      700 &]];
t = FixedPoint[b, start]  (* A192649 *)
Differences[t] (* A192650 *)