publication . Other literature type . Article . 2002

Random Generators and Normal Numbers

Bailey, David H.; Crandall, Richard E.;
Open Access English
  • Published: 01 Jan 2002
  • Publisher: A K Peters, Ltd.
Abstract
Pursuant to the authors' previous chaotic-dynamical model for random digits of fundamental constants, we investigate a complementary, statistical picture in which pseudorandom number generators (PRNGs) are central. Some rigorous results are achieved: We establish b-normality for constants of the form $\sum_i 1/(b^{m_i} c^{n_i})$ for certain sequences $(m_i), (n_i)$ of integers. This work unifies and extends previously known classes of explicit normals. We prove that for coprime $b,c>1$ the constant $\alpha_{b,c} = \sum_{n = c, c^2, c^3,\dots} 1/(n b^n)$ is b-normal, thus generalizing the Stoneham class of normals. Our approach also reproves b-normality for the K...
Subjects
free text keywords: Normal numbers, transcendental numbers, pseudo-random number generators, 11K16, 11K06, 11J81, 11K45, General Mathematics, Mathematical analysis, Normal number, Generalization, Combinatorics, Pseudorandom number generator, Integer, Uncountable set, Mathematics, Discrete mathematics, Coprime integers, Topology
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publication . Other literature type . Article . 2002

Random Generators and Normal Numbers

Bailey, David H.; Crandall, Richard E.;