Vol. 9, No. 1, 2020

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The sum-of-digits function on arithmetic progressions

Lukas Spiegelhofer and Thomas Stoll

Vol. 9 (2020), No. 1, 43–49
Abstract

Let s2 be the sum-of-digits function in base 2, which returns the number of nonzero binary digits of a nonnegative integer n. We study s2 along arithmetic subsequences and show that — up to a shift — the set of m-tuples of integers that appear as an arithmetic subsequence of s2 has full complexity.

Keywords
sum-of-digits function, arithmetic progression, Cusick's conjecture
Mathematical Subject Classification 2010
Primary: 11A63, 11B25
Milestones
Received: 19 September 2019
Revised: 26 November 2019
Accepted: 10 December 2019
Published: 20 February 2020
Authors
Lukas Spiegelhofer
Institute of Discrete Mathematics and Geometry
Vienna University of Technology
Vienna
Austria
Thomas Stoll
Institut Élie Cartan
Université de Lorraine
Vandœuvre-lès-Nancy
France