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A097048
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a(n) = least denominator Y of the proper fractions X/Y which need n or more terms as an Egyptian fraction.
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3
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OFFSET
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1,1
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COMMENTS
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These are the simplest proper fractions requiring n parts as an Egyptian fraction, where "simplest" means smallest denominator and the smallest numerator breaks ties: 1/2, 2/3, 4/5, 8/11, 16/17, 77/79, 732/733, ...
Checking just (p-1)/p for prime p finds no example requiring 9 parts for p <= 800399: see "results-single" in the github link. - Hugo van der Sanden, Feb 28 2015
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, D11
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LINKS
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EXAMPLE
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27538/27539 is the simplest rational that cannot be expressed as the sum of 7 or fewer distinct unit fractions. That is, no rational p/q requires 8 or more with 0 < p/q < 1, and either q < 27539 or (q = 27539 and p < 27538). - Hugo van der Sanden, Sep 14 2010
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CROSSREFS
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KEYWORD
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nonn,more,frac,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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