Let $n, m$ be integers. $m > 1, n > m$.
$$S = \left\lceil{\frac{n}{m}}\right\rceil + \left\lceil{\frac{1}{m}\left\lceil{\frac{n}{m}}\right\rceil}\right\rceil + \left\lceil{\frac{1}{m}}\left\lceil{\frac{1}{m}\left\lceil{\frac{n}{m}}\right\rceil}\right\rceil\right\rceil + \cdots + 1$$
Is there a closed form possible for S? I know a code for this is *very* easy, but I'm more interested in the "formula" than the code. Any help would be great. Thanks...