Non-standard binary representations and the Stern sequence

Joseph Vandehey; Katie Anders; Madeline Locus Dawsey; Rajat Gupta

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arxiv 2308.07448 v1 pith:ZHJ2DBUN submitted 2023-08-14 math.CO math.NT

Non-standard binary representations and the Stern sequence

Katie Anders , Madeline Locus Dawsey , Rajat Gupta , Joseph Vandehey This is my paper

classification math.CO math.NT

keywords binaryrepresentationsproofssequencesigned-digitsternbijectivederived

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We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$-th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this result can be derived from recent work of Monroe on binary signed-digit representations of a fixed length.

Non-standard binary representations and the Stern sequence

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