This probably isn't the most important question, but I'm working on something where I've found it convenient to define the following two functions (on the integers): $ I_o(q):= \begin{cases} q & q \text{ is odd } \\ q-1 & q \text{ is even} \end{cases} \qquad \text{ and } \qquad I_e(q):= \begin{cases} q & q \text{ is even } \\ q-1 & q \text{ is odd} \end{cases}. $
So $I_o(q)$ is just the largest odd number less than or equal to $q$ and $I_e(q)$ is the same, except for even numbers. I feel that I've seen this function before with a notation similar as to that of floor, but I've had little luck googling it. So I was curious if there was a common notation for this function.