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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. 3
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
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: A051300 A001127 A051299 * A119490 A013174 A283195
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 March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)