How to represent this coordinate sequence mathematically? Consider the 3 dimensional coordinate $(i, j, k)$. For every $i, j$ counts from $i, i + 1, i + 2$ etc, however, if it reaches a given parameter, say, B, the count resets to 1. Think of it as a sawtooth sort of. Meanwhile, k counts from 1, 2, 3,..., up to a predetermined number b.
As an example, assume $j = 9$, $B = 10$ and $b = 3$, $(i, \,j)$ will take the form:

$(9, 1) \, (10, 2) \,  (1, 3)$

I can represent the sequence if it is zero indexed using the modulus operator like so: $(j, 1), ((j + 1) \% \,B, 2)$. For example, the above sequence would be written as:

$(8, 0) \, (9, 1) \, (0, 2)$

However, I would like to count from 1 and not 0. How to do this?

Just add $1$ after you compute the modulus. Of course, to compensate, you need to compute the modulus of $j-1$. This yields the $k$th term of your sequence as:
$${\Large(}(j-1)\mathbin\%B +1, (i-1)\mathbin\% b+1{\Large)}$$
where it is understood that we first compute the modulus and then add $1$.
