

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



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
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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



