An example of a $P$-primary ideal $I$ satisfying $I^2 = IP$

Question

Give some examples of a $P$-primary ideal $I \not=P $ in a noetherian domain $R$ such that $I^2=PI $.

Answer 1

Let $R = k [[t^3, t^4, t^5]]$, $P = (t^3, t^4, t^5)$, and $I = (t^3, t^4)$. Then $$IP = I^2 = (t^6, t^7, t^8). $$