Eventual complexity formula for products of the form p(q3^j+1)

Let $\|n\|$ denote the complexity of a natural number, and let $p,q$ be natural numbers. Product complexity conjecture. For each pair of natural numbers $p$ and $q$, there exists $a\ge0$ such that, for $j\ge a$,

$$\|p(q3^j+1)\|=3j+1+\|p\|+\|q\|.$$

This is an eventual exact formula for a family of products whose complexity is studied through the tables in the paper; its status is based on observed cases only.