O násobení desetinných čísel
On a conjecture of Dekking : The sum of digits of even numbers
Let and denote by the sum-of-digits function in base . For considerIn 1983, F. M. Dekking conjectured that this quantity is greater than and, respectively, less than for infinitely many , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.
On a problem of Bednarek
We answer a question of Bednarek proposed at the 9th Polish, Slovak and Czech conference in Number Theory.
On a problem of Erdős and Graham concerning digits
On a problem of Frobenius for an almost consecutive set of integers.
On a problem of Tamas Varga
On binary representations of integers with digits .
On expansions of Gaussian integers with non-negative digits.
On Gelfond’s conjecture about the sum of digits of prime numbers
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 infinite series representations of real numbers
On linear normal lattices configurations
In this paper we extend Champernowne’s construction of normal numbers in base to the case and obtain an explicit construction of the generic point of the shift transformation of the set . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base .
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and 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
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 numbers containing each block infinitely often.
On Obláth's problem.
On Ramanujan expansions of certain arithmetical functions
On repdigit polygonal numbers.
On sequences of ±1's defined by binary patterns [Book]
On some Markov matrices arising from the generalized Collatz mapping
On strings of consecutive economical numbers of arbitrary length.