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A228855
Nodes of tree generated as follows: (2,3) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
4
2, 3, 5, 8, 11, 13, 18, 19, 21, 27, 29, 30, 31, 34, 41, 44, 46, 47, 49, 50, 55, 65, 67, 68, 71, 73, 75, 76, 79, 80, 81, 89, 100, 101, 106, 108, 109, 111, 112, 115, 116, 117, 119, 121, 123, 128, 129, 131, 144, 153, 157, 163, 165, 166, 171, 172, 173, 175, 176
OFFSET
1,1
LINKS
EXAMPLE
Taking the first generation of edges of the tree to be G(1) = {(2,3)}, the edge (2,3) grows G(2) = {(3,5), (3,8)}, which grows G(3) = {(5,8), (5,13), (8,11),(8,19)}, ... Expelling duplicate nodes and sorting leave {2,3,5,8,11,13,...}.
MATHEMATICA
f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; y = 3; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 05 2013
STATUS
approved