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 A097048 a(n) = least denominator Y of the proper fractions X/Y which need n or more terms as an Egyptian fraction. 1
 2, 3, 5, 11, 17, 79, 733, 27539 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, D11 LINKS David Eppstein, Ten Algorithms for Egyptian Fractions Hugo van der Sanden, code and results on github. EXAMPLE 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 CROSSREFS See A097049 for numerators. Sequence in context: A077497 A237995 A178606 * A286268 A244914 A227126 Adjacent sequences:  A097045 A097046 A097047 * A097049 A097050 A097051 KEYWORD nonn,more,frac,nice AUTHOR Ed Pegg Jr and Don Reble, Jul 21 2004 EXTENSIONS a(8) from Hugo van der Sanden, Sep 14 2010 STATUS approved

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