I am currently working on a problem where it is useful to consider the index of the last digit in a number which is not a $9$.
For example in the number $$a=8243848392842992999,$$ the index I care about is $3$ because the coefficient of $10^3$ is the first base-$10$ digit which is not a 9. $$a = 9 + 9 * 10 + 9 * 10^2 + 2 * 10^3 + \cdots.$$
More generally, we could ask the question in any base, for the first index of a $p$-ary digit which is not $p-1$. In base $3$, this might look something like $$b = 0120120220220212211112$$ having the index I care about being $1$ because $$b = 2 + 1*3 + \cdots.$$
I could call this the "first nonpenultimate digit" but that seems like a confusing name. I was wondering if a name for such an index had already been agreed upon?
Relying on Martin R's comment, for a prime $p$, it is the $p$-adic valuation of $b + 1$, denoted $v_p(b+1)$.