On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus, II.
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Jürgen Eichenauer-Herrmann (1993)
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Richard H. Hudson (1983)
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Jean-Marie De Koninck, Imre Kátai (2011)
Acta Arithmetica
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K.-K. Choi, M.-C. Liu, K.-M. Tsang (1992)
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Pieter Moree (1997)
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R.F. Tichy, P. Kirschenhofer (1986)
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J.F. Voloch, Arnaldo Garcia (1987)
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John B. Friedlander, Sergei Konyagin, Igor E. Shparlinski (2002)
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Richard Hudson (1973)
Acta Arithmetica
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R.F. Tichy, P. Kirschenhofer (1981)
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D. Landers, L. Rogge (1975)
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L. Carlitz, R. Scoville (1976)
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Jean-Marie De Koninck, Imre Kátai (2014)
Colloquium Mathematicae
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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.
Bruno Massé, Dominique Schneider (2014)
Acta Arithmetica
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We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.
Hoi H. Nguyen, Endre Szemerédi, Van H. Vu (2008)
Acta Arithmetica
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A. Ivic, Jean-Marie De Koninck (1979/80)
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Urs Würgler, Rolf Kultze (1986/87)
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Henri Faure (2005)
Acta Arithmetica
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