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A097049
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a(n) = least numerator X of the proper fractions X/A097048(n) which need n or more terms as an Egyptian fraction.
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1
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OFFSET
| 1,2
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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 ...
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, D11
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LINKS
| David Eppstein, Ten Algorithms for Egyptian Fractions
Hugo van der Sanden, Code
Hugo van der Sanden, Description of code
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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 (hv(AT)crypt.org), Sep 14, 2010.
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CROSSREFS
| See A097048 for denominators.
Sequence in context: A051300 A001127 A051299 * A119490 A013174 A098204
Adjacent sequences: A097046 A097047 A097048 * A097050 A097051 A097052
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KEYWORD
| nonn,more,frac
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AUTHOR
| Ed Pegg Jr. (edp(AT)wolfram.com) and Don Reble (djr(AT)nk.ca) Jul 21 2004
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EXTENSIONS
| a(8) from Hugo van der Sanden (hv(AT)crypt.org), Sep 14, 2010.
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