Arithmetical study of recurrence sequences
Asymptotique des récurrences mahlériennes : le cas cyclotomique
Nous étudions le comportement asymptotique d’une classe de suites mahlériennes dont les séries génératrices sont des produits infinis. Un exemple caractéristique est celui de l’estimation des coefficients de Taylor de , voisin des partitions binaires étudiées par De Bruijn. Le résultat obtenu illustre un cas typique d’une classification naturelle des suites mahlériennes. Les techniques utilisées, transformation de Mellin ou méthode du col, ressortissent à la théorie analytique des nombres et à...
Benford's law, values of L-functions and the 3x+1 problem
Beukers' integrals and Apéry's recurrences.
Bihyperbolic numbers of the Fibonacci type and their idempotent representation
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
Bounding squares in second order recurrence sequences
Bounds for frequencies of residues of second-order recurrences modulo
The authors examine the frequency distribution of second-order recurrence sequences that are not -regular, for an odd prime , and apply their results to compute bounds for the frequencies of -singular elements of -regular second-order recurrences modulo powers of the prime . The authors’ results have application to the -stability of second-order recurrence sequences.
Bounds for linear recurrences with restricted coefficients.
Bounds for the 3x+1 problem using difference inequalities
Calculs sur des suites récurrentes linéaires
Cholesky factorizations of matrices associated with -order recurrent sequences.
Cobalancing numbers and cobalancers.
Collatz cycles with few descents
Common terms in binary recurrences
The purpose of this paper is to prove that the common terms of linear recurrences and have at most common terms if , and have at most three common terms if where and are fixed positive integers and is a prime, such that neither nor is perfect square, further are nonzero integers satisfying the equations and .
Complementary equations.
Concatenations with binary recurrent sequences.
Congruences pour les nombres de Schröder
Convolution of second order linear recursive sequences II.
We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
Corrigendum: A note on self-conjugate -color partitions.
Decomposing rational numbers