For a set $I\subseteq \Bbb N$, defined $s_{I}(n)=\min\{i\in I\mid i>n\}$. The set $I$ is called polynomial-time-enumerable if $s_I(n)$ is computable in $\mathsf{poly}(n)$ time.
Most of the sets I can imagine are polynomial time enumerable. I am really looking for an example of a set of integers that is NOT polynomial time enumerable.
Thanks in advance.