One-Step-Ahead Prediction of Pseudorandom Number Generator

Hi guys, I've heard of machine learning before (and have a base knowledge) but have no idea how to go about using it to tackle my problem. Assume I have a bad pseudorandom number generator that has an underlying trend. Given n-1 previous observations, what methods would I use to predict the nth observation? Further, how do I assess whether the prediction was correct and change my model for the next observation?

What tools do I use? How do I asses the resulting model and improve upon it? In the end I actually don't need to predict the exact value of the subsequent observation, but predict it within a threshold, i.e., "will the next value be >50? >90? Does this turn it into an easier classification problem?

Thanks!