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A130738
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Greedy odd Egyptian fraction representation of 1 (without repeats).
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0
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3, 5, 7, 9, 11, 13, 23, 721, 979007, 661211444787, 622321538786143185105739, 511768271877666618502328764212401495966764795565, 209525411280522638000804396401925664136495425904830384693383280180439963265695525939102230139815
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) is the largest odd Egyptian fraction as yet unused, such that the sum of the Egyptian fractions so far does not exceed 1. The sum of a(n) is a greedy representation (greedy because each step bites off as much as possible) of 1, using only odd Egyptian fractions, all distinct.
Terms a(11)-a(13) were found by David Eppstein (see posting from Nov 09 1996), who says that he found them by applying EgyptOddGreedy[2/3,5] from his Egyptian fractions notebook.
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REFERENCES
| R. K. Guy, Unsolved Problems Number Theory, Sect D11.
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LINKS
| David Eppstein, Egyptian fractions
David Eppstein, Egyptian fractions, Discussion, Nov 09 1996.
Index entries for sequences related to Egyptian fractions
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EXAMPLE
| E.g. a(8)=721 because 1/721 is the largest odd Egyptian fraction less than 1-1/a(1)-1/a(2)-1/a(3)-1/a(4)-1/a(5)-1/a(6)-1/a(7).
1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/23 + 1/721 + 1/979007 + 1/661211444787 + 1/622321538786143185105739 + 1/511768271877666618502328764212401495966764795565 + 1/209525411280522638000804396401925664136495425904830384693383280180439963265695525939102230139815 = 1.
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CROSSREFS
| Cf. A002966, A169820.
Sequence in context: A030155 A143448 A039786 * A024323 A118820 A117521
Adjacent sequences: A130735 A130736 A130737 * A130739 A130740 A130741
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KEYWORD
| nonn,fini,full
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AUTHOR
| Jon Wild (wild(AT)music.mcgill.ca), Jul 06 2007
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EXTENSIONS
| Edited and a(11)-a(13) added by N. J. A. Sloane, May 29 2010, at the suggestion of Jan Szejko.
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