GCD(a(n),a(n-1)+a(n-2))=1

[Leroy Quet]

I just submitted the following sequence, where each term (from the third 
on) is coprime to the sum of the previous 2 terms.

I am suprised this sequence is not in the EIS. Did I make a mistake in 
calculating the terms by hand?

>A000001 1,2,4,5,7,11,13,17,19,23,25,29,31,37,3,9
>%N A000001 a(1) = 1, a(2) = 2. a(n) is lowest positive integer not among 
>earlier terms of the sequence where GCD(a(n),a(n-1)+a(n-2)) = 1.
>%C A000001 2 and 4 are the only even terms in the sequence.
>%e A000001 Of the positive integers not among the first 4 terms of the 
>sequence, 7 is the lowest which is coprime to a(3) + a(4) = 4 + 5 = 9.
>%O A000001 1
>%K A000001 ,more,nonn,


What I wonder is, is every odd positive integer in the sequence?

thanks,
Leroy Quet