Definition:Coherent Sequence

Definition
Let $p$ be a prime.

Let $\sequence{\alpha_n}$ be a sequence of integers such that:
 * $(1): \quad \forall n \in \N: 0 \le \alpha_n \le p^n - 1$
 * $(2): \quad \forall n \in \N: \alpha_{n + 1} \equiv \alpha_n \pmod {p^n}$

The sequence $\sequence{\alpha_n}$ is said to be a coherent sequence.

If it is necessary to emphasize the choice of prime $p$ then the sequence $\sequence{\alpha_n}$ is said to be a $p$-adically coherent sequence.