Smallest on a list

Initially the list contains the integer $1$. In each step, you delete the smallest element $x$ from the list and then add the elements $2x$ and $3x$ into the list. What is the smallest element of the list after $n$ steps?

For example when $n=5$, the list changes as follows:

$[1] \rightarrow [2,3] \rightarrow [3,4,6] \rightarrow [4,6,6,9] \rightarrow [6,6,9,8,12] \rightarrow [6,9,8,12,12,18]$

In this case, the smallest element at the end is $6$.

The time complexity of the algorithm should be $O(n \log n)$.

In a file twothree.py, implement a function smallest that returns the desired answer.

def smallest(n):
    # TODO

if __name__ == "__main__":
    print(smallest(1)) # 2
    print(smallest(5)) # 6
    print(smallest(123)) # 288
    print(smallest(55555)) # 663552