A note on weighted consecutive Davenport constant

Let G be a group and A⊆ [1,exp(G)-1]. We define the constant CA(G), which is the least positive integer such that every sequence over G of length at least has an A-weighted consecutive product-one subsequence. In this paper, among other things, we prove that CA(Cₙ²)=4 with $A=[1,n-1],$ and C(H× K)=|H||K|, where H is a finite abelian group and K is a metacyclic group.