A028229 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.

2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23

Offset

1,1

Comments

Graham showed that every number >=78 is strict-sense Egyptian.

References

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.

Links

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

Example

1=1/3+1/3+1/3, so 3+3+3=9 is Egyptian.

Mathematica

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 *)

Crossrefs

Cf. A051882. Complement gives A125726.

Sequence in context: A285528 A151894 A352328 * A104452 A335073 A344514

Adjacent sequences: A028226 A028227 A028228 * A028230 A028231 A028232

Keyword

nonn,fini,full,nice

Author

N. J. A. Sloane, Jud McCranie

Status

approved