5 problems
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Cusick's sum-of-digits conjecture
Cusick's conjecture. For every integer ,
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Median-preserving conjecture for the stopped-random-walk tree dynamics
Tree-asymmetry conjecture. For every ,
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The block-appending conjecture for the sum-of-digits correlation measure
Let be an odd integer, and let denote the correlation quantity associated with the binary sum-of-digits difference for . For each , consider the integer…
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The extremal block-length conjecture for the sum-of-digits correlation measure
Extremal block-length conjecture. For all such with we have
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Dekking's non-drifting conjecture for sums of digits of even numbers
Dekking's conjecture. The error term satisfies