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A228854 Nodes of tree generated as follows: (1,3) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.

%I A228854 #18 Jun 21 2018 02:14:16
%S A228854 1,3,4,7,10,11,15,17,18,24,25,26,27,29,37,40,41,43,44,47,56,58,61,63,
%T A228854 64,65,67,68,69,71,76,89,91,93,97,98,99,100,101,104,105,106,108,109,
%U A228854 111,112,115,123,137,138,140,147,149,152,153,154,155,157,159,160
%N A228854 Nodes of tree generated as follows: (1,3) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
%H A228854 Ivan Neretin, <a href="/A228854/b228854.txt">Table of n, a(n) for n = 1..10000</a>
%e A228854 Taking the first generation of edges of the tree to be G(1) = {(1,3)}, the edge (1,3) grows G(2) = {(3,4), (3,7)}, which grows G(3) = {(4,7), (4,11), (7,10),(7,17)}, ... Expelling duplicate nodes and sorting leave {1,3,4,7,10,11,...}.
%t A228854 f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 1; y = 3; t = {{x, y}};
%t A228854 u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
%t A228854 w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
%t A228854 Sort[Union[w]]
%Y A228854 Cf. A141832, A228853, A228855, A228856.
%K A228854 nonn,easy
%O A228854 1,2
%A A228854 _Clark Kimberling_, Sep 05 2013