Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Jun 21 2018 02:14:16
%S 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 64,65,67,68,69,71,76,89,91,93,97,98,99,100,101,104,105,106,108,109,
%U 111,112,115,123,137,138,140,147,149,152,153,154,155,157,159,160
%N 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 Ivan Neretin, <a href="/A228854/b228854.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 1; y = 3; t = {{x, y}};
%t u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
%t w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
%t Sort[Union[w]]
%Y Cf. A141832, A228853, A228855, A228856.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 05 2013