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The Rudin–Shapiro Sequence and Similar Sequences Are Normal Along Squares

Published online by Cambridge University Press:  20 November 2018

Clemens Müllner
Clemens Müllner*
Affiliation:
Institut für Diskrete Mathematik und Geometrie TU Wien, Wiedner Hauptstr. 8-10, 1040 Wien, Austria, e-mail: clemens.muellner@tuwien.ac.at
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Abstract

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We prove that digital sequences modulo $m$ along squares are normal, which covers some prominent sequences, such as the sum of digits in base $q$ modulo $m$, the Rudin–Shapiro sequence, and some generalizations. This gives, for any base, a class of explicit normal numbers that can be efficiently generated.

Keywords

11A6311B8511L0311N6060F05Rudin–Shapiro sequencedigital sequencesnormalityexponential sums
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 5 , 01 October 2018 , pp. 1096 - 1129
Copyright
Copyright © Canadian Mathematical Society 2018

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