jmc

Every positive integer appears at least once; if we consider an arbitrary integer $k$, it can be written in the form $\left(\genfrac{}{}{0ex}{}{k}{1}\right)$. Almost all integers can be written twice, because $\left(\genfrac{}{}{0ex}{}{k}{1}\right)=\left(\genfrac{}{}{0ex}{}{k}{k-1}\right)=k$, but when $k-1=1$, the two occurrences overlap into one. This takes place for $k=2$, and $2$ only appears once in Pascal's Triangle, because succeeding rows of Pascal's Triangle only contain $1$'s and numbers greater than $2$. Therefore, the minimum value of $f(n)$ is $\boxed{1}$.