The Rudin–Shapiro Sequence and Similar Sequences Are Normal Along Squares
- 1 October 2018
- journal article
- research article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 70 (5), 1096-1129
- https://doi.org/10.4153/cjm-2017-053-1
Abstract
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
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