The unexpected complexity of list letter markers

All indexes are zero-based.

• $x$ = input index.
• $s$ = size of the collection of available symbols (e.g. a, b, c, ..., z).
• $p$ = digit position from the right.
• $y$ = index of the symbol in the collection.

For the domain: $\set{x \in \mathbb{W} | x \geq o}$,

we can describe the algorithm with the function:

$f(x,s,p)=\lfloor \frac{x-o}{s^p} \rfloor \mod s$,

where: $o=\sum_{n=0}^p s^{n}-1$.

$o$ is the "digit offset", which compensates for two things:

• Zero-based input index ($-1$).
• Leading undefined values ($\sum_{n=0}^p s^{n}$).