Question 4
Peter and Jack went to a store to buy some pens. In the store, they are selling different pen packs such that each pack has exactly $1,2,4,8,16,\ldots$ pens. For example, if Peter wants to buy $14$ pens, then he needs to buy packs with $8$, $4$ and $2$ pens. It is known that Peter bought $n$ pens and Jack bought $n+1$ pens, where $n\le2019$. If Peter and Jack bought the minimum number of packs of pens and Peter has $4$ packs more than Jack, then find the number of different values of $n$.