Consider the sequence -1, 0, 2, 5, 7, 10, etc. where you add 2, then 3 and repeat. Somehow, it could be noted like "-1, 0, (+2, +3)*" à la regular expression. I can say this is an increasing integer sequence where the difference of two consecutive elements is ultimately periodic.
But clearly, there must be a shorter name to this kind of integer sequences somewhere in mathematic literature.
And even maybe there is already some short notation like I did with "-1, 0, (+2, +3)*".
Can you provide bibliographic references for such integer sequences, please ?
I'm not sure if this answers your question in the way you're looking for, but the sequence you have listed is described by the Online Encyclopedia of Integer Sequences (https://oeis.org) as "Integers that are congruent to $\{2, 3\}$ mod $5$". The specific page for your sequence is https://oeis.org/A047215 and I definitely recommend checking out the site more since it's very cool.
There are a number of formulas listed on the above article which might help you characterize your sequence in a broader sense, or just without mod arithmetic if that's what you're looking for.
Hope this helps!