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A028229
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Call m Egyptian if we can partition m = x_1+x_2+...+x_k into positive integers x_i such that Sum_{i=1..k} 1/x_i = 1; sequence gives all non-Egyptian numbers.
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4
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2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. L. Graham, A theorem on partitions, J. Austral. Math. Soc., 4 (1963), 435-441.
J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 147.
See also R. K. Guy, Unsolved Problems Number Theory, Sect. D11.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Egyptian fractions
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EXAMPLE
| 1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.
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CROSSREFS
| Cf. A051882. Complement gives A125726.
Sequence in context: A191167 A006431 A151894 * A104452 A062877 A068526
Adjacent sequences: A028226 A028227 A028228 * A028230 A028231 A028232
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KEYWORD
| nonn,fini,full,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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EXTENSIONS
| Graham showed that every number >=78 is strict-sense Egyptian.
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