I'm trying to generate a seemingly random list of integers without the use of a computational device; one capable of being unraveled with a mathematical function. What's the best way to devise a complex function algorithm that produces seemingly unrelated results? My goal is to be able to create a list of numbers (e.g. 327965184) that look as if they can't be related in any way, but can be solved one by one by plugging in sequential numbers (for x) in an f(x) function (e.g. f(1)=3, f(2)=2, f(3)=7).
Thanks for your help.
Here's a particular favorite of mine: it requires some math, but is pretty manageable by hand.
Take a random seed of length $n$, and square it, and then pull out the middle $n$ digits of $n^2$ to serve as the next number in the pseudorandom sequence.