A228856 - OEIS

%I #18 Nov 03 2024 17:07:45

%S 1,2,3,5,7,8,9,11,12,13,14,16,17,18,19,21,22,23,25,26,27,29,30,31,33,

%T 34,35,36,37,39,41,43,44,45,46,47,49,50,52,53,55,56,57,59,60,61,62,63,

%U 64,65,66,67,68,69,70,71,73,74,75,76,77,79,80,81,83,84

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

%H Ivan Neretin, <a href="/A228856/b228856.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) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5), (2,7)}, which grows G(3) = {(3,5), (3,8), (3,11), (5,7), (5,12), (5,17), (7,9), (7,16), (7,23)}, ... Expelling duplicate nodes and sorting leave {1,2,3,5,7,8,9,...}.

%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 1,2

%A _Clark Kimberling_, Sep 05 2013