13. 设$a>0$且$a\ne 1$，已知数列$\{b_{n}\}$满足${b_n}=\left\{{\left.\begin{array}{l}{(3-a)n-2,n\leqslant 6}\\ {{a^{n-5}},n>6}\end{array}\right.}\right.$，且$\{b_{n}\}$是递增数列，则$a$的取值范围是 $(2,3)$ ．