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

Author

Anonymous

Keywords

• nonn
• fini
• full

Comments

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

References

• Joe Roberts, Lure of the Integers, entry 239.

Links

• 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

Crossrefs

Subsequence of A018888.

Programs

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 *)

Extensions

Corrected by Arlin Anderson.

Additional comments from Jud McCranie.

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