The Rudin–Shapiro Sequence and Similar Sequences Are Normal Along Squares
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 ge...
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| Veröffentlicht in: | Canadian journal of mathematics 2018-10, Vol.70 (5), p.1096-1129 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0008-414X 1496-4279 |
| DOI: | 10.4153/CJM-2017-053-1 |