## Functiones et Approximatio Commentarii Mathematici

### Construction of normal numbers by classified prime divisors of integers II

#### Abstract

Given an integer $q\ge 2$, a $q$-normal number is an irrational number $\eta$ such that any preassigned sequence of $k$ digits occurs in the $q$-ary expansion of $\eta$ at the expected frequency, namely$1/q^k$. In a series of recent papers, using the complexity of the multiplicative structure of integers along with a method we developed in 1995 regarding the distribution of subsets of primes in the prime factorization of integers, we initiated new methods allowing for the creation of large families of normal numbers. Here, we further expand on this initiative.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 7-27.

Dates
First available in Project Euclid: 20 September 2013

https://projecteuclid.org/euclid.facm/1379686431

Digital Object Identifier
doi:10.7169/facm/2013.49.1.1

Mathematical Reviews number (MathSciNet)
MR2895156

Zentralblatt MATH identifier
1283.11109

#### Citation

De Koninck, Jean-Marie; Kátai, Imre. Construction of normal numbers by classified prime divisors of integers II. Funct. Approx. Comment. Math. 49 (2013), no. 1, 7--27. doi:10.7169/facm/2013.49.1.1. https://projecteuclid.org/euclid.facm/1379686431

#### References

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• J.M. De Koninck and I. Kátai, Construction of normal numbers by classified prime divisors of integers, Functiones et Approximatio 45.2 (2011), 231–253.
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