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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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5
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2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23
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OFFSET
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1,1
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COMMENTS
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Graham showed that every number >=78 is strict-sense Egyptian.
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REFERENCES
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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
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Table of n, a(n) for n=1..13.
R. L. Graham, A theorem on partitions, J. Austral. Math. Soc. 3:4 (1963), pp. 435-441. doi:10.1017/S1446788700039045
Eric Weisstein's World of Mathematics, Egyptian Number.
Index entries for sequences related to Egyptian fractions
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EXAMPLE
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1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.
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MATHEMATICA
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egyptianQ[n_] := Select[ IntegerPartitions[n], Total[1/#] == 1 &, 1] =!= {}; A028229 = Reap[ Do[ If[ !egyptianQ[n], Sow[n]], {n, 1, 40}]][[2, 1]] (* Jean-François Alcover, Feb 23 2012 *)
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CROSSREFS
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Cf. A051882. Complement gives A125726.
Sequence in context: A006431 A285528 A151894 * A104452 A335073 A062877
Adjacent sequences: A028226 A028227 A028228 * A028230 A028231 A028232
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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N. J. A. Sloane, Jud McCranie
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STATUS
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approved
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