The investigation of primes in certain arithmetic sequences is one of the fundamental problems in number theory and especially, finding blocks of distinct primes has gained a lot of attention in recent years. In this context, we prove the existence of long blocks of k-wise coprime elements in certain regular sequences. More precisely, we prove that for any positive integers \(H \ge k \ge 2\) and for a real-valued k-times continuously differentiable function \(f \in \mathcal {C}^k\left( [1, \infty )\right) \) satisfying \(\lim _{x \rightarrow \infty } f^{(k)}(x) = 0\) and \(\limsup _{x \rightarrow \infty } f^{(k-1)}(x) = \infty \) , there exist infinitely many positive integers n such that \(\begin{aligned} \gcd \left( \lfloor f(n+i_1)\rfloor , \lfloor f(n+i_2)\rfloor , \cdots , \lfloor f(n+i_k)\rfloor \right) ~=~ 1 \end{aligned}\) for any integers \(1 \le i_1< i_2< \cdots < i_k \le H\) . Further, we show that there exists a subset \(\mathcal {A}\subseteq \mathbb {N}\) having upper Banach density one such that \(\begin{aligned} \gcd \left( \lfloor f(n_1) \rfloor , \lfloor f(n_2) \rfloor , \cdots , \lfloor f(n_k) \rfloor \right) ~=~ 1 \end{aligned}\) for any distinct integers \(n_1, n_2, \cdots , n_k \in \mathcal {A}.\)
