Strictly increasing function on positive integers giving value between $100$ and $200$ I'm looking for some sort of function $f$ that can take any integer $n>0$ and give a real number $100 \le m \lt 200$ such that if $a \lt b$ then $f(a) \lt f(b)$. How can I do that? I'm a programmer and I need this for an application of mine.

$f(n)=200-2^{-n}$ satisfies your criteria.
