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- W4386794265 abstract "Given a positive rational number $n/d$ with $d$ odd, its odd greedy expansion starts with the largest odd denominator unit fraction at most $n/d$, adds the largest odd denominator unit fraction so the sum is at most $n/d$, and continues as long as the sum is less than $n/d$. It is an open question whether this expansion always has finitely many terms. Given a fixed positive integer $n$, we find all reduced fractions with numerator $n$ whose odd greedy expansion has length $2$. Given $m-1$ odd positive integers, we find all rational numbers whose odd greedy expansion has length $m$ and begins with these numbers as denominators. Given $m-2$ compatible odd positive integers, we find an infinite family of rational numbers whose odd greedy expansion has length $m$ and begins with these numbers as denominators." @default.
- W4386794265 created "2023-09-16" @default.
- W4386794265 creator A5019249255 @default.
- W4386794265 creator A5063427751 @default.
- W4386794265 date "2023-09-13" @default.
- W4386794265 modified "2023-10-01" @default.
- W4386794265 title "Rational numbers with odd greedy expansion of fixed length" @default.
- W4386794265 doi "https://doi.org/10.48550/arxiv.2309.07280" @default.
- W4386794265 hasPublicationYear "2023" @default.
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