<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of integers. They prove in particular that the summatory function of this sequence has the “root <italic>N</italic>” property, analogously to the summatory function of the Golay-Shapiro sequence. We prove here that the root <italic>N</italic> property does not hold if we twist the sequence by powers of a complex number of modulus one, hence showing a fundamental difference with the Golay-Shapiro sequence.</p></abstract>

A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of integers. They prove in particular that the summatory function of this sequence has the “root N” property, analogously to the summatory function of the Golay-Shapiro sequence. We prove here that the root N property does not hold if we twist the sequence by powers of a complex number of modulus one, hence showing a fundamental difference with the Golay-Shapiro sequence.

On a Golay-Shapiro-Like Sequence

CNRS, Institut de Mathématiques, de Jussieu-PRG, Université Pierre et Marie Curie, Case 247, 4 Place Jussieu, F-75252 Paris Cedex 05,

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On a Golay-Shapiro-Like Sequence"}

A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of...

On a Golay-Shapiro-Like Sequence

Data publikacji: 13 sty 2017

Zakres stron: 205 - 210

Otrzymano: 25 mar 2016

Przyjęty: 25 lip 2016

DOI: https://doi.org/10.1515/udt-2016-0021

Słowa kluczowe
binary expansion, digital sequence, Rudin-Shapiro sequence, summatory function

© 2016 Jean-Paul Allouche, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a Golay-Shapiro-Like Sequence

Data publikacji: 13 sty 2017

Zakres stron: 205 - 210

Otrzymano: 25 mar 2016

Przyjęty: 25 lip 2016

DOI: https://doi.org/10.1515/udt-2016-0021

Słowa kluczowebinary expansion, digital sequence, Rudin-Shapiro sequence, summatory function

© 2016 Jean-Paul Allouche, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Słowa kluczowe
binary expansion, digital sequence, Rudin-Shapiro sequence, summatory function