6 citations · 12 across the 15 of their papers we have counts for
15 papers · 1 filter
A Padovan-automatic description of a nested recurrence
Benoit Cloitre, Haobo Ma, Wenlin Zhang
We study the sequence , and for , listed as A076502 in the On-Line Encyclopedia of Integer Sequences. We identify as a two…
Regular Arithmetic Functions, Volume I. Theory, Applications, Examples
Benoit Cloitre
This is the first of two volumes on regular arithmetic functions, and an introduction to their theory. A regular arithmetic function (RAF) is a kernel whose properties come from a…
Fibonacci, Dirichlet, and Gauss in a single sum
Benoit Cloitre
We study the fractional-part sums , where is the th Fibonacci number. Their asymptotic behavior depends on the parity of . For odd , the r…
The Thue-Morse Transform
Benoit Cloitre
We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^…
Beatty solutions of almost Golomb functional equations
Benoit Cloitre
We study the almost Golomb equation of order , , where , for nondecreasing sequences of positive integers. Its greedy solu…
The Mantovanelli-Hofstadter Sequence
Benoit Cloitre
We study the perturbed Hofstadter recurrence introduced by Mantovanelli, , with $\w…
Meta-automatic Sequences
John M. Campbell, Benoit Cloitre
Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are…
A Tauberian characterization of the Riemann hypothesis through the floor function
Benoit Cloitre
We introduce a new Tauberian framework through the theory of "regular arithmetic functions". This allows us to establish a characterization of the Riemann hypothesis by linking the…
On some identities in multiplicative number theory
Olivier Bordellès, Benoit Cloitre
Using elementary means, we prove several identities involving the Möbius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
Good variation theory: a tauberian approach to the Riemann Hypothesis
Benoit Cloitre
In this short note I present a tauberian conjecture that I consider to be the simplest and the best tauberian reformulation of RH using good variation theory. The method applies al…
Beyond odious and evil
Jean-Paul Allouche, Benoit Cloitre, Vladimir Shevelev
In a recent post on the Seqfan list the third author proposed a conjecture concerning the summatory function of odious numbers (i.e., of numbers whose sum of binary digits is odd),…
A tauberian approach to RH
Benoit Cloitre
The aim of this paper is twofold. Firstly we present our main discovery arising from experiments which is the tauberian concept of functions of good variation (FGV). Secondly we pr…
10 conjectures in additive number theory
Benoit Cloitre
Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searc…
Sloping Binary Numbers: A New Sequence Related to the Binary Numbers
David Applegate, Benoit Cloitre, Philippe Deléham +1
If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) ha…
Numerical Analogues of Aronson's Sequence
Benoit Cloitre, N. J. A. Sloane, Matthew J. Vandermast
Aronson's sequence 1, 4, 11, 16, ... is defined by the English sentence ``t is the first, fourth, eleventh, sixteenth, ... letter of this sentence.'' This paper introduces some num…