This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A228897 #6 Sep 10 2013 03:18:26
%S A228897 1,2,3,4,5,6,8,9,10,12,13,15,16,18,20,21,24,26,30,32,34,35,39,40,42,
%T A228897 48,52,54,55,60,63,66,68,70,72,75,84,88,89,90,96,102,104,108,110,112,
%U A228897 117,126,130,135,136,138,144,145,150,160,165,168,174,176,178
%N A228897 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,x+y) and (y,x*y) are edges.
%C A228897 The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not). The extreme branches are (1,2)->(2,3)->(3,5)->(5,8)->... and (1,2)->(2,4)->(4,8)->(8,32)->... These branches contribute to A228897, as subsequences, the Fibonacci numbers, A000045, and the sequence 2^(A000045) = A000302.
%e A228897 Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,4)}, which grows G(3) = {(3,5), (3,6), (4,6), (4,8)}, ... Expelling duplicate nodes and sorting leave (1, 2, 3, 4, 5, 6, 8, 9, 10, 12,...).
%t A228897 f[x_, y_] := {{y, x + y}, {y, x* y}}; x = 1; y = 2; t = {{x, y}};
%t A228897 u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
%t A228897 w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
%t A228897 Sort[Union[w]]
%Y A228897 Cf. A228853.
%K A228897 nonn,easy
%O A228897 1,2
%A A228897 _Clark Kimberling_, Sep 08 2013