I have seen different things from difference sources. For example, in "Factorizations of $b^n\pm 1$", the rank of N is used to mean the first term in $b^n-1$ it divides. Is this unique to this sequence because it would be synonymous with multiplicative order in this case? For example, https://stackoverflow.com/questions/9223901/what-is-position-in-terms-of-a-sequence, states that rank refers to the number of terms less than a number in a sequence. Also in this link, it says that "position" refers to the position specific number in the sequence, of course, but not necessarily the first term a number $N$ $divides$.
Edit: If there is no ubiquitous term for this, could I simply call it a $primitive$ $index$, as it refers to the term for which a number is a $primitive$ $divisor$? Or is this somehow incorrect or ignorant-sounding?