I have an equation related to some work I'm doing on Poisson distribution where I'm calculating a sequence of 100 values between a minimum and maximum value which is set by another formula. Unfortunately I don't really understand this area of maths, but I'm trying to resolve this equation to use in a computer calculation.
Let $m$ be the minimum value and $M$ be the maximum value (which are given).
$n$, $m$ and $M$ are all integers. f(n) is also rounded to an integer value.
For $n=1$, $$ f(n) = \min(m,1) $$
For values of $1<n\leq100$ this is the formulae $$\large{ f(n) = \min\Biggl\lgroup\biggl\lgroup\frac{M}{f(n-1)}\biggr\rgroup^{\frac{1}{101-n}} \cdot (n-1) , n\Biggr\rgroup }$$
My question is - is there a way to implement this function/equation that doesn't rely on knowing the value of $f(n-1)$ - knowing $n$, $M$, and $m$.
An example sequence for $m=1$, $M=847$ is at http://pastebin.com/PvQgNg7i