A Permutation Based On Largest Odd Divisor

[Leroy Quet]

I just submitted the following to the EIS.

%S A000001 1,2,3,6,7,12,8,4,5,14,17,28,18,21
%N A000001 a(1) = 1; a(n) = (largest odd divisor of a(n-1))th lowest 
positive integer not yet in the sequence.
%C A000001 It seems likely, but not certain, that this sequence is a 
permutation of the positive integers, which it is if and only if there 
are an infinite number of powers of 2 in the sequence.
%e A000001 a(6) = 12, and the highest odd divisor of 12 is 3. Among the 
first 6 terms of the sequence is not 4, 5, 8, 9,..., and the 3rd of these 
is 8, which is therefore a(7).
%O A000001 1
%K A000001 ,more,nonn,
%A A000001 Leroy Quet (qq-quet at mindspring.com), Dec 23 2004


Is this a permutation of the positive integers?

(If someone proves this to be or to not be a permutation, could they then 
amend the comment line? thanks.)

thanks,
Leroy Quet