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Abstract
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Let
be the sum-of-digits
function in base
,
which returns the number of nonzero binary digits of a nonnegative integer
. We
study
along arithmetic subsequences and show that — up to a shift — the set of
-tuples
of integers that appear as an arithmetic subsequence of
has
full complexity.
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Keywords
sum-of-digits function, arithmetic progression, Cusick's
conjecture
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Mathematical Subject Classification 2010
Primary: 11A63, 11B25
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Milestones
Received: 19 September 2019
Revised: 26 November 2019
Accepted: 10 December 2019
Published: 20 February 2020
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