I feel like this is far simpler than I am making it.
I am looking for a function $y=f(x)$ such that:
$f(1) = 1$
$f(2) = 1 $
$f(3) = 3 $
$f(4) = 3 $
$f(5) = 5 $
$f(6) = 5$
That is to say, all the evens become the preceding odd number. Does this function exist? If so, what is it? Lastly, how would a mathematician write it?