A228855 - OEIS

%I #16 Jun 20 2018 19:18:36

%S 2,3,5,8,11,13,18,19,21,27,29,30,31,34,41,44,46,47,49,50,55,65,67,68,

%T 71,73,75,76,79,80,81,89,100,101,106,108,109,111,112,115,116,117,119,

%U 121,123,128,129,131,144,153,157,163,165,166,171,172,173,175,176

%N 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.

%H Ivan Neretin, <a href="/A228855/b228855.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) = {(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,...}.

%t f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; 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, A228854, A228856.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 05 2013