How can we find a function for a conversion table with the following properties? The range of both inputs and outputs is $[0..100]$; inputs are integers.
$f(0) = 0$ $f(100) = 100$ $f(1) - f(0) = 2(f(100) - f(99))$
So, $f(1)$ should be $1.\bar3$ and $f(99)$ should be $99.\bar3$. The difference between subsequent outputs is linearly decreasing, so $f(50)-f(49)\approx 1$.