On a Golay-Shapiro-Like Sequence

Jean-Paul Allouche

doi:10.1515/udt-2016-0021

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On a Golay-Shapiro-Like Sequence

Uniform distribution theory

Volume 11 (2016): Issue 2 (December 2016)

By: Jean-Paul Allouche

Open Access

|Jan 2017

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.

References

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2016-0021 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 205 - 210

Submitted on: Mar 25, 2016

Accepted on: Jul 25, 2016

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

binary expansion,

digital sequence,

Rudin-Shapiro sequence,

summatory function

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Jean-Paul Allouche, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 11 (2016): Issue 2 (December 2016)