Permutation? Floor Of Ratio Of Adjacent Terms = 2

[Leroy Quet]

First, thanks to everyone who contributed to the
last discussion I started.

Now a new topic.

I just submitted this:

%S A139080 1,2,4,8,3,6,12,5,10,20,7,14,28,11,22,9
%N A139080 a(1)=1. a(n) = the smallest positive
integer not occurring earlier in the sequence
such that
floor(max(a(n),a(n-1))/min(a(n),a(n-1))) = 2.
%C A139080 Is there always an unused positive
integer, a(n), such that
floor(max(a(n),a(n-1))/min(a(n),a(n-1))) = 2, or
does the sequence terminate? If the sequence is
infinite, is it a permutation of the positive
integers?
%O A139080 1
%K A139080 ,more,nonn,

(I find the sequence to be more beautiful than is
suggested at first glance by its definition.)

The question I have is, as seen in the comment
line:

Is there always an unused positive integer, a(n),
such that
floor(max(a(n),a(n-1))/min(a(n),a(n-1))) = 2, or
does the sequence terminate? If the sequence is
infinite, is it a permutation of the positive
integers?

And of course I must ask, did I make a mistake
with the terms I give?

Thanks,
Leroy Quet




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