On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus, II.

Jürgen Eichenauer-Herrmann

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On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus.

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Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.