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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

Table of n, a(n) for n=1..8.

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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Last modified November 18 05:08 EST 2017. Contains 294853 sequences.