  For a finite dimensional algebra $A$ with $0 < \phi dim (A) = m < \infty$ we
prove that there always exist modules $M$ and $N$ such that $\phi(M) = m-1$ and
$\phi (N) = 1$. On the other hand, we see an example of an algebra that not
every value between $1$ and its $\phi$-dimension is reached by the $\phi$
function. We call that values gaps and we prove that the algebras with gaps
verifies the finitistic conjecture.
