

A192645


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 and 2 are in S.


5



1, 2, 3, 5, 8, 16, 21, 24, 39, 55, 60, 63, 135, 185, 192, 231, 247, 252, 255, 320, 369, 377, 416, 432, 437, 440, 512, 551, 567, 572, 575, 944, 945, 1080, 1265, 1457, 1496, 1504, 1512, 1517, 1520, 1521, 1889, 2079, 2448, 2449, 2495, 2584, 2631, 2639
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OFFSET

1,2


COMMENTS

See A192476 for a general discussion. Related sequences:
A192645: f(x,y) = x^2  y^2 > 0, start={1,2};
A192647: f(x,y) = x^2  y^2 > 0, start={1,3};
A192648: f(x,y) = x^2  y^2 > 0, start={2,3};
A192649: f(x,y) = x^2  y^2 > 0, start={1,2,4}.


LINKS



EXAMPLE

2^2  1^2 = 3;
3^2  2^2 = 5, 3^2  1^2 = 8;
5^2  3^2 = 16, 5^2  2^2 = 21, 5^2  1^2 = 24.
Taking the generating procedure in the order just indicated results in the monotonic ordering of the sequence and also suggests a triangular format for the generated terms:
3;
5, 8;
16, 21, 24;
39, 55, 60, 63;
135, 185, 192, 231, 247;
...


MATHEMATICA

start = {1, 2};
f[x_, y_] := If[MemberQ[Range[1, 5000], 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}]]]], # <
5000 &]];
t = FixedPoint[b, start] (* A192645 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



