Notation for "modulo-like indexing"

Question

I have indexed sequence $(A_i)_{i=0,1,...,n,...}$, and want to say that $A_i$ is $A_j$ itself if $i \equiv j\pmod n$. What is the formal mathematical notation for this?

Answer 1

The set of equivalence classes modulo $n$ is typically denoted $\mathbb Z/n \mathbb Z$. You can write $(A_i)_{i \in \mathbb Z/n\mathbb Z}$.