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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. 3
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
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: A237995 A333081 A178606 * A286268 A359630 A244914
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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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)