Let $O(f(n))$ be the minimum time complexity for output a real sequence $\{a_i\}$.
The input of the algorithm is a integer $n$. It output the finite sequence $a_1, a_2, \ldots, a_n$. (Clearly $f(n)\geq n$.)
What can we say about the time complexity of
\begin{equation*} \max(a_1, a_2, \ldots, a_n)? \end{equation*}
Is there always an algorithm to solve this problem in time complexity less than $O(f(n))$?
For example, the algorithm that output the sequence of natural numbers is a $O(n)$ algorithm. Finding the maximum value between 1 and n is $O(1)$.
If we have some more information, like Kolmogorov complexity of the sequence, how will it change the time bounds?
It seems that if a sequence can be described easily, we can find a way to find the maximum value easier than naively compute the sequence and compare.