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We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number $β$ in $(1, 2)$ is univoque and self-sturmian if and only if the $β$ -expansion of $1$ is of the form $1 v$ , where $v$ is a characteristic...

A note on univoque self-Sturmian numbers

Jean-Paul Allouche (2010)

RAIRO - Theoretical Informatics and Applications

We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic...

Let $p$ be a prime number. In this paper we prove that the addition in $p$ -ary without carry admits a recursive definition like in the already known cases $p = 2$ and $p = 3$ .

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A bound on Kaprekar constants.

A combinatorial method for construction normal numbers.

A conjecture on digital cycles.

A decision method for the recognizability of sets defined by number systems

A generalization of a theorem by Cheo and Yien concerning digital sums.

A generalization of Hasse's generalization of the Syracuse algorithm

A Good Basis for Computing with Complex Numbers.

A Markov approach to the generalized Syracuse algorithm

A negative answer to two questions about the smallest prime numbers having given digital sums.

A New Infinite Product Representation for Real Numbers.

A note on linear recurrent Mahler numbers.

A note on the parity of the sum-of-digits function.

A note on univoque self-sturmian numbers

A note on univoque self-Sturmian numbers

A polynomial inequality generalising an integer inequality.

A propos du théorème de Cassels-Schmidt concernant de nombres normaux

A recursive definition of $p$ -ary addition without carry

A result on the digits of aⁿ

A self-similar tiling generated by the minimal Pisot number

A Summation Formula Related to the Binary Digits.

Currently displaying 1 – 20 of 38