A228897 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,x+y) and (y,x*y) are edges.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 21, 24, 26, 30, 32, 34, 35, 39, 40, 42, 48, 52, 54, 55, 60, 63, 66, 68, 70, 72, 75, 84, 88, 89, 90, 96, 102, 104, 108, 110, 112, 117, 126, 130, 135, 136, 138, 144, 145, 150, 160, 165, 168, 174, 176, 178

Offset

1,2

Comments

The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not). The extreme branches are (1,2)->(2,3)->(3,5)->(5,8)->... and (1,2)->(2,4)->(4,8)->(8,32)->... These branches contribute to A228897, as subsequences, the Fibonacci numbers, A000045, and the sequence 2^(A000045) = A000302.

Links

Table of n, a(n) for n=1..61.

Example

Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,4)}, which grows G(3) = {(3,5), (3,6), (4,6), (4,8)}, ... Expelling duplicate nodes and sorting leave (1, 2, 3, 4, 5, 6, 8, 9, 10, 12,...).

Mathematica

f[x_, y_] := {{y, x + y}, {y, x* y}}; x = 1; 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. A228853.

Sequence in context: A245027 A065108 A094563 * A068095 A064390 A229461

Adjacent sequences: A228894 A228895 A228896 * A228898 A228899 A228900

Keyword

nonn,easy

Author

Clark Kimberling, Sep 08 2013

Status

approved