How does the number of partitions of $k$ relate to the number of partitions of $k + 1$ whose smallest part is one?
I used to think it would be similar to prime numbers since the number of partitions of $1,2,3,4,5$ goes $1,2,3,5,7$ respectively but as $k$ increases, the number of partitions get much larger and eventually non-prime. However, I don't know how to answer this question on how $k$ compares to $k+1$.