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On a conjecture of Dekking : The sum of digits of even numbers

Iurie Boreico, Daniel El-Baz, Thomas Stoll (2014)

Journal de Théorie des Nombres de Bordeaux

Let q 2 and denote by s q the sum-of-digits function in base q . For j = 0 , 1 , , q - 1 consider # { 0 n < N : s q ( 2 n ) j ( mod q ) } . In 1983, F. M. Dekking conjectured that this quantity is greater than N / q and, respectively, less than N / q for infinitely many N , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.

On a problem of Bednarek

Florian Luca (2012)

Communications in Mathematics

We answer a question of Bednarek proposed at the 9th Polish, Slovak and Czech conference in Number Theory.

On Gelfond’s conjecture about the sum of digits of prime numbers

Joël Rivat (2009)

Journal de Théorie des Nombres de Bordeaux

The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.

On linear normal lattices configurations

Mordechay B. Levin, Meir Smorodinsky (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper we extend Champernowne’s construction of normal numbers in base b to the d case and obtain an explicit construction of the generic point of the d shift transformation of the set { 0 , 1 , . . . , b - 1 } d . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base b .

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny (2010)

RAIRO - Theoretical Informatics and Applications

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

On Obláth's problem.

Gica, Alexandru, Panaitopol, Laurenţiu (2003)

Journal of Integer Sequences [electronic only]

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