The fractional part of and Beatty sequences
The function and some well-known sequences.
The Gergonne -pile trick and the base counting system. (El truco de pilas de Gergonne y el sistema de numeración de base .)
The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature
The greatest common divisor of two recursive functions.
The Haar measure of certain sets in the Bohr group
The Hankel transform and some of its properties.
The Haros-Farey sequence at two hundred years. A survey.
The independence number of a subset of an Abelian group.
The integer sequence A002620 and upper antagonistic functions.
The intersection of recurrence sequences
The inverse problem for representation functions for general linear forms.
The joint distribution of the binary digits of integer multiples
The Josephus problem
We give explicit non-recursive formulas to compute the Josephus-numbers and and explicit upper and lower bounds for (where ) which differ by (for the bounds are even better). Furthermore we present a new fast algorithm to calculate which is based upon the mentioned bounds.
The jumping champions of the Farey series
The -binomial transforms and the Hankel transform.
The Kazandzidis supercongruences. A simple proof and an application
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The Lagrange inversion formula and divisibility properties.
The largest subset in [1,n] whose integers have pairwise l.c.m. not exceeding n, II