On the average growth of random Fibonacci sequences.
On the bases with an exact order
On the behavior of a variant of Hofstadter's -sequence.
On the central coefficients of Bell matrices.
On the class of all reciprocal bases for integers.
On the coefficients of the asymptotic expansion of .
On the Collatz conjecture
We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
On the commutator lengths of certain classes of finitely presented groups.
On the complexity of infinite sequences. (Sur la complexité des suites infinies.)
On the composite Lehmer numbers with prime indices, III
On the concentration of points on modular hyperbolas and exponential curves
On the conjectures of Rauzy and Shallit for infinite words
We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
On the critical pair theory in ℤ/pℤ
On the cycle structure of linear recurring sequences.
On the Davenport constant and group algebras
For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence over G such that for all . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for which (G) -...
On the degree of an irreducible factor of the Bernoulli polynomials
On the degree of regularity of generalized van der Waerden triples.
On the degrees of irreducible factors of higher order Bernoulli polynomials
On the densities of sets of multiples.
On the density of languages representing finite set partitions.