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
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