A097049 a(n) = least numerator X of the proper fractions X/A097048(n) which need n or more terms as an Egyptian fraction.

1, 2, 4, 8, 16, 77, 732, 27538

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

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: A001127 A374734 A051299 * A119490 A013174 A283195

Adjacent sequences: A097046 A097047 A097048 * A097050 A097051 A097052

Keyword

nonn,more,frac

Author

Ed Pegg Jr and Don Reble, Jul 21 2004

Extensions

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

Status

approved