Say you have this sequence of examples:
2^0 = 1
2^1 = 2
2^1 + 2^0 = 3
2^2 = 4
2^2 + 2^0 = 5
2^2 + 2^1 + 2^0 = 6
2^3 - 2^0 = 7
2^3 = 8
...
There is some equation in there for going from the output integer like $6$ to the shortest input equation like $2^2 + 2^1$, where the base digit is always 2. So these seem like polynomial equations where $ax$ is always 2. I am wondering how to figure out automatically what equation any integer will turn into.