A018890 Numbers whose smallest expression as a sum of positive cubes requires exactly 7 cubes.

7, 14, 21, 42, 47, 49, 61, 77, 85, 87, 103, 106, 111, 112, 113, 122, 140, 148, 159, 166, 174, 178, 185, 204, 211, 223, 229, 230, 237, 276, 292, 295, 300, 302, 311, 327, 329, 337, 340, 356, 363, 390, 393, 401, 412, 419, 427, 438, 446, 453, 465, 491, 510, 518, 553, 616

Offset

1,1

Comments

It is conjectured that a(121)=8042 is the last term. - Jud McCranie

An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that if there are any terms beyond a(121) = 8042, they are greater than 1.62 * 10^34. - Charles R Greathouse IV, Jan 23 2014

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 306.

Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics, Princeton Science Library, 1994. See p. 53.

J. Roberts, Lure of the Integers, entry 239.

Links

T. D. Noe, Table of n, a(n) for n = 1..121

F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Math. Comp. 68 (1999), pp. 1303-1310.

Jan Bohman and Carl-Erik Froberg, Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.

K. S. McCurley, An effective seven-cube theorem, J. Number Theory, 19 (1984), 176-183.

Eric Weisstein's World of Mathematics, Cubic Number

Eric Weisstein's World of Mathematics, Waring's Problem

Index entries for sequences related to sums of cubes

Mathematica

Select[Range[700], (pr = PowersRepresentations[#, 7, 3]; pr != {} && Count[pr, r_/; (Times @@ r) == 0] == 0)&] (* Jean-François Alcover, Jul 26 2011 *)

Crossrefs

Cf. A004829, A018888, A018889.

Sequence in context: A100451 A028555 A061823 * A118502 A190367 A246172

Adjacent sequences: A018887 A018888 A018889 * A018891 A018892 A018893

Keyword

nonn,fini,changed

Author

Anonymous

Status

approved