Let $R$ be a commutative Noetherian $k$-algebra which is an integral domain and let $I$ be an ideal of $R$, $I:=\langle a_1,\ldots,a_n \rangle$ with $a_1,\ldots,a_n \in R$ a regular sequence.
Assume that $b_1,\ldots,b_m \in R$ also generate $I$, namely: $I=\langle b_1,\ldots,b_m \rangle$.
When $b_1,\ldots,b_m$ is a regular sequence? Probably not always?
Perhaps the following questions are relevant: i and ii.
Any hints and comments are welcome!