Also in this series: Tiling rectangles with F pentomino plus rectangles
The goal is to tile rectangles as small as possible with the N pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one N-pentomino will tile. Example shown, with the $1\times 1$, you can tile a $2\times 4$ as follows:
Now we don't need to consider $1\times 1$ any longer as we have found the smallest rectangle tilable with copies of N plus copies of $1\times 1$.
There are at least 22 more solutions. More expected. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging.