A228896 Nodes of tree generated as follows: (3,2) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.

2, 3, 5, 7, 9, 12, 16, 17, 19, 23, 25, 26, 29, 31, 34, 39, 41, 43, 45, 46, 50, 55, 57, 59, 62, 63, 64, 66, 69, 70, 71, 74, 75, 81, 84, 85, 91, 93, 94, 97, 98, 99, 101, 104, 105, 107, 109, 111, 112, 116, 117, 119, 121, 127, 131, 133, 139, 140, 143, 147, 148

Offset

1,1

Comments

The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

Taking the first generation of edges to be G(1) = {(3,2)}, the edge (3,2) grows G(2) = {(2,5), (2,7)}, which grows G(3) = {(5,7), (5,12), (7,9), (7,16)}, ... Expelling duplicate nodes and sorting leave (2,3,5,7,9,12,...).

Mathematica

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 2; 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. A228856.

Sequence in context: A293230 A133231 A235111 * A281783 A224854 A074752

Adjacent sequences: A228893 A228894 A228895 * A228897 A228898 A228899

Keyword

nonn,easy

Author

Clark Kimberling, Sep 08 2013

Status

approved