A228855 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.

2, 3, 5, 8, 11, 13, 18, 19, 21, 27, 29, 30, 31, 34, 41, 44, 46, 47, 49, 50, 55, 65, 67, 68, 71, 73, 75, 76, 79, 80, 81, 89, 100, 101, 106, 108, 109, 111, 112, 115, 116, 117, 119, 121, 123, 128, 129, 131, 144, 153, 157, 163, 165, 166, 171, 172, 173, 175, 176

Offset

1,1

Links

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

Example

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,...}.

Mathematica

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; 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]]

Crossrefs

Cf. A141832, A228853, A228854, A228856.

Sequence in context: A117725 A106637 A246361 * A171048 A209292 A185371

Adjacent sequences: A228852 A228853 A228854 * A228856 A228857 A228858

Keyword

nonn,easy

Author

Clark Kimberling, Sep 05 2013

Status

approved