$$
\begin{array}{l}
A=\left\{x \mid \log _{2}(x-1)<1\right\}, \\
B=\{x|| x-a \mid<2\} .
\end{array}
$$

If $A \cap B \neq \varnothing$, then the range of real number $a$ is
$\qquad$
-1. $(-1,5)$.
From $\log _{2}(x-1)<1 \Rightarrow A=(1,3)$,
$$
|x-a|<2 \Rightarrow B=(a-2, a+2) \text {. }
$$

If $A \cap B=\varnothing$, then
$a+2 \leqslant 1$ or $a-2 \geqslant 3$
$\Rightarrow a \leqslant-1$ or $a \geqslant 5$.
Therefore, when $A \cap B \neq \varnothing$, the range of values for $a$ is $(-1,5)$.