Challenge of the Week - Random Numbers

Most random number generators use an algorithm a(k 1) f(a(k)) to produce a sequence of integers a(1), a(2), etc. that behaves like random numbers. The function f is integer-valued and bounded; because of these two conditions, the sequence a(k) eventually becomes periodic for k large enough. This is an undesirable property, and many public random number generators (those built in Excel, Python, and other languages) are poor and not suitable for cryptographic applications, Markov Chains Monte-Carlo associated with hierarchical Bayesian models, or large-scale Monte-Carlo simulations to detect extreme events (example: fraud detection, big data context). It's easy to build a sequence of non-periodic numbers or digits, by using irrational numbers. By construction, this decimal number has no period.