A228856 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,y+x), (y,2y+x), and (y,3y+x) are edges.

1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 39, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84

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) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5), (2,7)}, which grows G(3) = {(3,5), (3,8), (3,11), (5,7), 5,12), 5,17), (7,9), (7,16), (7,23)}, ... Expelling duplicate nodes and sorting leave {1,2,3,5,7,8,9,...}.

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: A226811 A227802 A329780 * A274688 A053661 A171944

Adjacent sequences: A228853 A228854 A228855 * A228857 A228858 A228859

Keyword

nonn,easy

Author

Clark Kimberling, Sep 05 2013

Status

approved