Find a closed form solution for the following sequence 1,2,1,3,2,4,2,6,3,8,3,12

Question

I need help with this problem.

Find a closed form solution for the following sequence 1,2,1,3,2,4,2,6,3,8,3,12

Answer 1

Seems to be of the form $1,2,1,3,\ldots,k,2^k,k,3\cdot 2^{k-1},\ldots$. However, there are infinitely many sequences with "reasonably good definitions" which start with a given finite subsequence. The sequence given by projectilemotion is a perfectly good one.