Smallest on a list

The list initially contains a single integer 1. In each round, you remove the smallest element x from the list, and add the values 2x and 3x to the list. What is the smallest value on the list after n rounds? You may assume that n is at most 10^5.

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]

Here the smallest value at the end is 6.

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

def smallest(n):
    # TODO

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