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 A228898 #5 Sep 10 2013 03:17:53
%S A228898 1,2,3,5,7,8,12,13,16,19,21,29,31,34,39,45,50,55,63,73,74,81,89,97,
%T A228898 112,119,131,144,155,160,178,185,186,191,193,205,212,233,236,246,257,
%U A228898 283,297,312,343,369,377,391,398,417,425,441,469,479,482,505,524,555
%N A228898 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^2 + y^2) are edges.
%C A228898 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)->(2,5)->(5,29)->(29,866)->... These branches contribute to A228898, as subsequences, the Fibonacci numbers, A000045, and A000283.
%e A228898 Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5)}, which grows G(3) = {(3,5), (3,13), (5,7), (5,29)}, ... Expelling duplicate nodes and sorting leave (1, 2, 3, 5, 7, 8, 12, 13, 16, 19,...).
%t A228898 f[x_, y_] := {{y, x + y}, {y, x^2 + y^2}}; x = 1; y = 2; t = {{x, y}};
%t A228898 u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {18}]; v = Flatten[u];
%t A228898 w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
%t A228898 Sort[Union[w]]
%Y A228898 Cf. A228853, A000045.
%K A228898 nonn,easy
%O A228898 1,2
%A A228898 _Clark Kimberling_, Sep 08 2013