Let $J$ be an ideal in a Noetherian local ring $(R,m)$. It is well known that for any prime ideal $p\in Spec(R)$, $l(J_p)\leq l(J)$, where $l(J)$ is the analytic spread of $J$.
Q) Are there examples of ideals $J$ such that $l(J_p)\leq l(J)-1$ for all $p\supset J$ such that $ht p=ht J+1$ and $J^n\neq J^{(n)}$ for some $n$ (where $J^{(n)}$ is the nth symbolic power)?