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ON A PROBLEM ON NORMAL NUMBERS RAISED BY IGOR SHPARLINSKI

Published online by Cambridge University Press:  16 June 2011

JEAN-MARIE DE KONINCK*
Affiliation:
Dép. de mathématiques et de statistique, Université Laval, Québec, Québec G1V 0A6, Canada (email: jmdk@mat.ulaval.ca)
IMRE KÁTAI
Affiliation:
Computer Algebra Department, Eötvös Loránd University, 1117 Budapest, Pázmány Péter Sétány I/C, Hungary (email: katai@compalg.inf.elte.hu)
*
For correspondence; e-mail: jmdk@mat.ulaval.ca
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Abstract

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Given an integer d≥2, a d-normal number, or simply a normal number, is an irrational number whosed-ary expansion is such that any preassigned sequence, of length k≥1, taken within this expansion occurs at the expected limiting frequency, namely 1/dk. Answering questions raised by Igor Shparlinski, we show that 0.P(2)P(3)P(4)…P(n)… and 0.P(2+1)P(3+1)P(5+1)…P(p+1)…, where P(n) stands for the largest prime factor of n, are both normal numbers.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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