The Rudin-Shapiro sequence and similar sequences are normal along squares

2017/04/21 by Müllner, Clemens
#11B85 #11L03 #60F05 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11A63 #Secondary: 11N60

paper · doi:10.48550/arxiv.1704.06472

Abstract

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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