8. Let two strictly increasing sequences of positive integers $\left\{a_{n}\right\},\left\{b_{n}\right\}$ satisfy: $a_{10}=b_{10}<2017$, for any positive integer $n$, there is $a_{n+2}=a_{n+1}+a_{n}, b_{n+1}=2 b_{n}$, then all possible values of $a_{1}+b_{1}$ are $\qquad$ .
$$
\begin{array}{l}
a_{10}=a_{9}+a_{8}=2 a_{8}+a_{7}=3 a_{7}+2 a_{6}=5 a_{6}+3 a_{5}=8 a_{5}+5 a_{4}=13 a_{4}+8 a_{3} \\
=21 a_{3}+13 a_{2}=34 a_{2}+21 a_{1},
\end{array}
$$

Since $b_{10}=b_{1} \cdot 2^{9}=512 b_{1}, \\ a_{2}=-8 \times 1536+21 t>0\end{array} \Rightarrow 586 \leqslant t \leqslant 587\right.$.
When $t=587$, $\left\{\begin{array}{l}a_{1}=10, \\ a_{2}=39 .\end{array}\right.$ When $t=586$, $\left\{\begin{array}{l}a_{1}=44, \\ a_{2}=18\end{array}\right.$ (discard).
When $b_{1}=2$, $b_{10}=512 \times 2=1024 \Rightarrow 34 a_{2}+21 a_{1}=1024$
The general solution of equation (2) is $\left\{\begin{array}{l}a_{1}=13 \times 1024-34 t>0, \\ a_{2}=-8 \times 1024+21 t>0\end{array} \Rightarrow t=391 \Rightarrow\left\{\begin{array}{l}a_{1}=18, \\ a_{2}=19 .\end{array}\right.\right.$
When $b_{1}=1$, $b_{10}=512 \Rightarrow 34 a_{2}+21 a_{1}=512$
The general solution of equation (3) is $\left\{\begin{array}{l}a_{1}=13 \times 512-34 t>0, \\ a_{2}=-8 \times 512+21 t>0\end{array} \Rightarrow t\right.$ has no solution.
In summary, all possible values of $a_{1}+b_{1}$ are 13, 20.