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).
This challenge involves identifying natural transcendental numbers with expansions (series, continued fractions) converging very fast to easily produce the decimals of the numbers in question. It starts with Log 10 - 2 Log 3 an a series that produces one new digit for each new term.
In this challenge, you will learn how to build non-periodic, high-quality random number generators, test the strength of your random number generator, and design generators that are easy to implement, fit for big data and extreme events simulation, and run fast. Dr. Vincent Granville has promised to participate, so this should add more fun to this challenge.
Here's the URL: http://bit.ly/1mvDXsz
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