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

1,2

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) = {(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,...}.

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]]

Crossrefs

Cf. A141832, A228853, A228855, A228856.

Sequence in context: A003669 A047342 A334469 * A257508 A221975 A340603

Adjacent sequences: A228851 A228852 A228853 * A228855 A228856 A228857

Keyword

nonn,easy

Author

Clark Kimberling, Sep 05 2013

Status

approved