Egyptian Fractions with Denominators from Sequences Closed Under Doubling
David Eppstein
Department of Computer Science
University of California, Irvine
Irvine, CA 92697
USA
Abstract:
Resolving a conjecture of Zhi-Wei Sun, we prove that every rational number
can be represented as a sum of distinct unit fractions whose denominators
are practical numbers. The same method applies to allowed denominators
that are closed under multiplication by two and include a multiple of
every positive integer, including the odious numbers, evil numbers,
Hardy-Ramanujan numbers, Jordan-Pólya numbers, and fibbinary numbers.
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(Concerned with sequences
A000069
A000695
A001013
A001969
A003714
A005153
A025487
A116882
A126684
A178757
A300867.)
Received July 19 2021; revised version received September 23 2021.
Published in Journal of Integer Sequences,
September 24 2021.
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