It is known that the [Somos-$k$ sequences](http://mathworld.wolfram.com/SomosSequence.html) for $k\ge 8$ do not give integers. But the first terms of **Somos-8** sequence $s\_n=a\_n/b\_n$
$$1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 13, 25, 61, 187, 775, 5827, 14815,\frac{420514}{7}, \frac{28670773}{91}$$
defined by $s\_1=s\_2=s\_3=s\_4=s\_5=s\_6=s\_7=s\_8=1$,
$$s\_{n+8}s\_n=s\_{n+7}s\_{n+1}+s\_{n+6}s\_{n+2}+s\_{n+5}s\_{n+3}+s\_{n+4}^2\qquad(n\ge1)$$
have only odd denominators $b\_n$. Morever $s\_n$ has even numerator $a\_n$ only for $n=9k$. It was checked for $n\le 67$. First terms of $s\_n\mod 8:=a\_n\cdot b\_n^{-1}\mod 8$ are
$$\begin{array}{l}
1, 1, 1, 1, 1, 1, 1, 1, {\bf 4},\\
7, 5, 1, 5, 3, 7, 3, 7, {\bf 6},\\
7, 7, 5, 7, 5, 3, 1, 1, {\bf 6},\\
5, 1, 5, 5, 3, 3, 7, 1, {\bf 4},\\
7, 7, 3, 3, 7, 7, 3, 1, {\bf 2},\\
1, 3, 1, 3, 7, 5, 3, 5, {\bf 2},\\
5, 7, 3, 7, 7, 3, 7, 3, {\bf 0},\\
1, 3, 7, 3,\ldots\end{array}$$


Is it possible to prove that the sequence $s\_n\mod 2$ is periodic?


**EDT.** It was found by მამუკა ჯიბლაძე that numerator of $s\_{71}$ is even while that of $s\_{72}$ is odd. The last line of the table above is
$$1, 3, 7, 3, 1, 5, 1, {\bf 2}, 5$$
So the conjecture about numerators of $s\_n$ is wrong. But the qustion about periodicity is still valid.



Is Somos-8 $\mod 2$ periodic?
I confirm the observation of @მამუკაჯიბლაძე that $\nu\_2(s\_{103})=-1$. That is, $s\_n\bmod 2$ is not well-defined at first place, which invalidates the question.


Moreover, for $n\geq 133$, $\nu\_2(s\_n)$ seems to form a strictly decreasing function, i.e., $s\_n$ accumulates larger and larger powers of $2$ in the denominators.


