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math.CO2023
Non-standard binary representations and the Stern sequence
Katie Anders, Madeline Locus Dawsey, Rajat Gupta +1
We show that the number of short binary signed-digit representations of an integer is equal to the -th term in the Stern sequence. Various proofs are provided, including dir…
math.NT2023
Representations of integers as quotients of sums of distinct powers of three
Katie Anders, Madeline Locus Dawsey, Bruce Reznick +1
Which integers can be written as a quotient of sums of distinct powers of three? We outline our first steps toward an answer to this question, beginning with a necessary and almost…