There is a really simple mapping between recurrent sequences and functions. Simply, given a function $f: A -> A$ that is, a function that outputs from the set i

There is a really simple mapping between recurrent sequences and functions. Simply, given a function $f: A -> A$ that is, a function that outputs from the set it gets input from. We then have the sequence $x_n+1 = f(x_n)$. Often, when dealing with incremental algorithms, the notation x' = f(x) is used. Here x' (pronounced x prime) stands for "the next value of x". It's a nice balance between the correctness of using indices and the conciseness of leaving them out. Going to a higher level, the sequence x' = f(x) is essentially trying to find a fixed point of the function f. To look at this in an actual for or while loop, you need to consider the stopping condition of the loop as part of the function.