

A097048


a(n) = least denominator Y of the proper fractions X/Y which need n or more terms as an Egyptian fraction.


1




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 (p1)/p for prime p finds no example requiring 9 parts for p <= 800399: see "resultssingle" 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 (djr(AT)nk.ca), Jul 21 2004


EXTENSIONS

a(8) from Hugo van der Sanden, Sep 14 2010


STATUS

approved



