Functiones et Approximatio Commentarii Mathematici

Construction of normal numbers by classified prime divisors of integers

Jean-Marie De Koninck and Imre Kátai

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Abstract

Given an integer $d\ge 2$, a $d$-{\it normal number}, or simply a {\it normal number}, is a real number whose $d$-ary expansion is such that any preassigned sequence, of length $k\ge 1$, of base $d$ digits from this expansion, occurs at the expected frequency, namely $1/d^k$. We construct large families of normal numbers using classified prime divisors of integers.

Article information

Source
Funct. Approx. Comment. Math., Volume 45, Number 2 (2011), 231-253.

Dates
First available in Project Euclid: 12 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.facm/1323705815

Digital Object Identifier
doi:10.7169/facm/1323705815

Mathematical Reviews number (MathSciNet)
MR2895156

Zentralblatt MATH identifier
1264.11068

Subjects
Primary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Secondary: 11N37: Asymptotic results on arithmetic functions 11A41: Primes

Keywords
normal numbers primes shifted primes arithmetic function

Citation

De Koninck, Jean-Marie; Kátai, Imre. Construction of normal numbers by classified prime divisors of integers. Funct. Approx. Comment. Math. 45 (2011), no. 2, 231--253. doi:10.7169/facm/1323705815. https://projecteuclid.org/euclid.facm/1323705815


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