A note on weighted consecutive Davenport constant

Let G be a group and A 1, (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.