I'm doing a research that is related to the fields of forcasting, time series etc.
I know that a sequence of the type $$\forall n>0: a_n=a_{n+k}$$ where $k$ is constant, such as $30,31,29,30,31,29...$ ($k=3$) is called periodic sequence or a sequence with cyclic behaviour.
How should i call a sequence that performs $$\forall m>0: a_n=a_{n+mk}$$ not necessarily $\forall n>0$, like the one in the headline? ($k=2$, $a_1=30$)
And how should i call a sequence that performs $$ Q>m>0: a_n=a_{n+mk}$$ where $Q\in\mathbb{R}$? (the same properties only with $m$ bounded by a finite number).