%I #9 Sep 09 2013 11:39:41

%S 2,3,5,7,9,12,16,17,19,23,25,26,29,31,34,39,41,43,45,46,50,55,57,59,

%T 62,63,64,66,69,70,71,74,75,81,84,85,91,93,94,97,98,99,101,104,105,

%U 107,109,111,112,116,117,119,121,127,131,133,139,140,143,147,148

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

%C The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not).

%H Vincenzo Librandi, <a href="/A228896/b228896.txt">Table of n, a(n) for n = 1..1000</a>

%e Taking the first generation of edges to be G(1) = {(3,2)}, the edge (3,2) grows G(2) = {(2,5), (2,7)}, which grows G(3) = {(5,7), (5,12), (7,9), (7,16)}, ... Expelling duplicate nodes and sorting leave (2,3,5,7,9,12,...).

%t f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 2; 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. A228856.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 08 2013