A228854 Nodes of tree generated as follows: (1,3) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.

1, 3, 4, 7, 10, 11, 15, 17, 18, 24, 25, 26, 27, 29, 37, 40, 41, 43, 44, 47, 56, 58, 61, 63, 64, 65, 67, 68, 69, 71, 76, 89, 91, 93, 97, 98, 99, 100, 101, 104, 105, 106, 108, 109, 111, 112, 115, 123, 137, 138, 140, 147, 149, 152, 153, 154, 155, 157, 159, 160

Offset: 1

Author

Clark Kimberling, Sep 05 2013

Keywords

• nonn
• easy

Examples

			Taking the first generation of edges of the tree to be G(1) = {(1,3)}, the edge (1,3) grows G(2) = {(3,4), (3,7)}, which grows G(3) = {(4,7), (4,11), (7,10),(7,17)}, ... Expelling duplicate nodes and sorting leave {1,3,4,7,10,11,...}.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A141832, A228853, A228855, A228856.

Programs

Mathematica

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 1; y = 3; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]