Induction · Superchallenge problem

A proof checks only $P(1)$ and proves both "$P(k) \Rightarrow P(k + 4)$" and "$P(k) \Rightarrow P(k + 7)$" for every $k \ge 1$. For how many $n$ with $1 \le n \le 100$ is $P(n)$ NOT established?