A defined Sequence

Let ( $a_n$ ) be a finite sequence with $9$ terms $a_1,a_2,a_3,....a_9$ defined as follows: $a_n = \begin{cases} 1 & \quad \text{if } n \text{ occurs infinitely many times in decimal expansion of} \frac{11}{6} \\ 2 & \quad \text{if } n \text{ occurs an odd numbers of times in the decimal expansion of} \frac{11}{6} \\ 3 & \quad \text{if } n \text{ occurs an even number of times or doesn't occur in the decimal expansion of} \frac{11}{6} \end{cases}$

Find largest no. of terms having identical value