The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse
sequence (Allouche and Cosnard 2000), is one of a number of related sequences of …

We introduce and study two analogs of one of the best known sequence in Mathematics:
Thue-Morse sequence. The first analog is concerned with the parity of number of runs of 1's …

In this note, we investigate the delta sequence associated to the classical Thue-Morse
sequence and prove a conjecture about the delta sequence. Further, we generalize the …

1.1. The Thue-Morse dynamical system. Let (tr) r∈ N and (tr) r∈ N be the sequences of
words on the alphabet {0, 1} defined by t0= 0, t0= 1, tr+ 1= trtr, and tr+ 1= trtr (in all this paper …

The Prouhet-Thue-Morse sequence, more commonly called the Thue-Morse (TM) sequence,
is defined on the alphabet∑={0, 1} and was first considered by Prouhet in 1851 [9]. The …

Abstract We introduce generalized Thue-Morse numbers of the form π β (θ):=∑ n= 1∞ θ n β
n where β∈(1, m+ 1] with m∈ N and θ=(θ n) n≥ 1∈{0, 1,⋯, m} N is a generalized Thue …

GENERALISATIONS DE LA SUITE DE THUE-MORSE 1. Introduction. La suite `a valeurs dans
Z/2Z de Thue-Morse t = (t(n)) définie p Page 1 Ann. Sci. Math. Québec 21 (1997), no. 2 …

We consider a class of binary sequences that generalize the Thue-Morse sequence. In
particular, we investigate the occurrences of palindromes in such sequences. We also …

Let sk (n) be the sum of digits of the expansion of the integer n in base k. Motivated by
certain identities of Nieto, and Bateman and Bradley involving sums of the form i= 0^ 2^ n-1 …

[1609.07999] Evaluating the Fabius function Skip to main content Cornell University Served
from the cloud We gratefully acknowledge support from the Simons Foundation, member …