What are the largest pairs of $p$-smooth integers with a difference of one?

Question

This is an interesting question because for very small $p$, we already know the answer: for $p = 2, 3, 5, 7$, the answers are $1$ and $2$, $8$ and $9$, $80$ and $81$, and $4374$ and $4375$, respectively. Is there a formula for these kind of numbers for higher $p$, an algorithm with bounded time/space, or, failing that, at least an entry for this on OEIS?

Answer 1

Yes, you can derive it from A145606. I found it by searching on $80,4374$ from your post. The OEIS entry observes that the list is not monotonic, so you would replace $5142500$ with $11859210$ as both $11859210,11859211$ are $19$ smooth and $5142500$ is the entry for $23$ smooth