A018889 Numbers whose shortest representation as a sum of positive cubes requires exactly 8 cubes.

15, 22, 50, 114, 167, 175, 186, 212, 231, 238, 303, 364, 420, 428, 454

Offset

1,1

Comments

Wieferich proved that 167 is the unique prime in this sequence. - Jonathan Vos Post, Sep 23 2006

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.

Joe Roberts, Lure of the Integers, entry 239.

Links

Table of n, a(n) for n=1..15.

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

G. L. Honaker, Jr. and Chris Caldwell, et al., A Prime Curios Page.

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, Warings Problem

Index entries for sequences related to sums of cubes

Mathematica

max = 500; nn = Union[(#*#).# & /@ Tuples[Range[0, 7], {7}]][[1 ;; max]]; Select[{#, PowersRepresentations[#, 8, 3]} & /@ Complement[Range[max], nn] , #[[2]] != {} &][[All, 1]] (* Jean-François Alcover, Jul 21 2011 *)

Crossrefs

Subsequence of A018888.

Sequence in context: A006615 A114867 A109288 * A186525 A236107 A065728

Adjacent sequences: A018886 A018887 A018888 * A018890 A018891 A018892

Keyword

nonn,fini,full

Author

Anonymous

Extensions

Corrected by Arlin Anderson.

Additional comments from Jud McCranie.

Edited by N. J. A. Sloane, Aug 10 2022

Status

approved