A228939 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,x*y) and (y,x^2 + y^2) are edges.

1, 2, 4, 5, 8, 10, 16, 20, 29, 32, 50, 68, 80, 125, 128, 145, 256, 320, 416, 500, 544, 640, 866, 1088, 1250, 1600, 2048, 2600, 4205, 4688, 5120, 6464, 6800, 8192, 8320, 15725, 16640, 21866, 25000, 25114, 34816, 36992, 51200, 66560, 102656, 128000, 130000

Offset: 1

Author

Clark Kimberling, Sep 08 2013

Keywords

• nonn
• easy

Examples

			Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,2), (2,5)}, which grows G(3) = {(2,4), (2,8), (5,10), (5,29)}, ... Expelling duplicate nodes and sorting leave (1, 2, 4, 5, 8, 10, 16, 20, 29, 32,...).
		

Crossrefs

Cf. A228853, A228939.

Programs

Mathematica

f[x_, y_] := {{y, x* y}, {y, x^2 + y^2}}; x = 1; y = 2; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {18}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]