

A097049


a(n) = least numerator X of the proper fractions X/A097048(n) which need n or more terms as an Egyptian fraction.


1




OFFSET

1,2


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, ...


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
Hugo van der Sanden, Description of code


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 A097048 for denominators.
Sequence in context: A051300 A001127 A051299 * A119490 A013174 A283195
Adjacent sequences: A097046 A097047 A097048 * A097050 A097051 A097052


KEYWORD

nonn,more,frac


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



