The Rudin-Shapiro sequence and similar sequences are normal along squares
classification
🧮 math.NT
keywords
normalsequencesalongbasemodulorudin-shapirosequencesome
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We prove that digital sequences modulo $m$ along squares are normal, which covers some prominent sequences like 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.
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