I have a problem as follows. Given $t_1\leq \cdots \leq t_k$ a non-decreasing sequence of integers, let $s_1<\cdots< s_k$ be another sequence of integers so that $t_i\leq s_i$ for every $i=1,\ldots ,k$. What is the minimum value of $s_k$?
There is an algorithm to find the minimum value of $s_k$ for each input $(t_1, \ldots ,t_k)$, however I prefer to have a closed formula for that value.
Can someone help me? Thanks a lot!
Looks like $$\max\{\,t_i+k-i\mid 1\le i\le k\,\} $$ to me.