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A097049 a(n) = least numerator X of the proper fractions X/A097048(n) which need n or more terms as an Egyptian fraction. 1
1, 2, 4, 8, 16, 77, 732, 27538 (list; graph; refs; listen; history; text; internal format)
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, Jul 21 2004

EXTENSIONS

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

STATUS

approved

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Last modified November 18 09:17 EST 2017. Contains 294879 sequences.