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

1,2

Links

Table of n, a(n) for n=1..47.

Example

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,...).

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]]

Crossrefs

Cf. A228853, A228939.

Sequence in context: A133020 A133075 A018433 * A115831 A094958 A018565

Adjacent sequences: A228936 A228937 A228938 * A228940 A228941 A228942

Keyword

nonn,easy

Author

Clark Kimberling, Sep 08 2013

Status

approved