Prove that there are infinitely many odd number can't be written as $pq-p-q$ Let $p$ and $q$ are prime.

Problem
Are there infinitely many odd positive integer $a$, which can't be written as $pq-p-q$ ?

Example $13$ can't be expressed in $pq-p-q$.
Sequence $13,25,33,37,49,53,61,67,73,75,85,93,97,109,...$
It looks there are infinitely many  and clearly  any even positive integer can't be expressed in $pq-p-q$. Thanks for your time to go through it.

Just choose $a=12k+1$ for any $k \in \mathbb{N}$. If $a=pq-p-q \implies a+1 = (p-1)(q-1)$. Clearly, we have $4 \nmid (a+1)$. Since $4 \nmid (p-1)(q-1)$ , WLOG we have $q=2$. This gives:
$$a=p-2 \implies 12k+3=p$$
which is clearly a contradiction as LHS is divisible by $3$.
