13. Define the recursive sequence $\left\{F_{n}\right\}$ :
$$
F_{0}=0, F_{1}=1 \text {, }
$$
$F_{n}(n \geqslant 2)$ is the remainder of $F_{n-1}+F_{n-2}$ divided by 3, i.e., the sequence $\left\{F_{n}\right\}: 0,1,1,2,0,2,2,1,0, \cdots$.
Then the value of $\sum_{i=2017}^{2024} F_{i}$ is ( ).
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
13. D.
$$
\begin{array}{l}
\text { Given } F_{n+8} \equiv F_{n+7}+F_{n+6} \equiv 2 F_{n+6}+F_{n+5} \\
\equiv 3 F_{n+5}+2 F_{n+4} \equiv 2 F_{n+4} \equiv 2 F_{n+3}+2 F_{n+2} \\
\equiv 4 F_{n+2}+2 F_{n+1} \equiv F_{n+2}+2 F_{n+1} \\
\equiv 3 F_{n+1}+F_{n} \equiv F_{n}(\bmod 3)
\end{array}
$$
$\Rightarrow\left\{F_{n}\right\}$ is a periodic sequence, with period $T=8$.
$$
\begin{array}{l}
\text { Therefore, } \sum_{i=2017}^{2024} F_{i}=\sum_{i=1}^{8} F_{i} \\
=0+1+1+2+0+2+2+1=9 .
\end{array}
$$