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A018889 Shortest representation as sum of positive cubes requires exactly 8 cubes. 9


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

%N Shortest representation as sum of positive cubes requires exactly 8 cubes.

%C Wieferich proved that 167 is the unique prime in this sequence. - _Jonathan Vos Post_, Sep 23 2006

%D J. Bohman and C.-E. Froberg, Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.

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

%D Joe Roberts, Lure of the Integers, entry 239.

%H G. L. Honaker, Jr. and Chris Caldwell, et al., <a href="http://primes.utm.edu/curios/page.php?short=167">A Prime Curios Page</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Warings Problem</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%t max = 500; nn = Union[(#*#).# & /@ Tuples[Range[0, 7], {7}]][[1 ;; max]]; Select[{#, PowersRepresentations[#, 8, 3]} & /@ Complement[Range[max], nn] , #[[2]] != {} &][[All, 1]] (* _Jean-Fran├žois Alcover_, Jul 21 2011 *)

%Y Subsequence of A018888.

%K nonn,fini,full,nice

%O 1,1

%A Anon

%E Corrected by Arlin Anderson (starship1(AT)gmail.com). Additional comments from _Jud McCranie_.

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Last modified December 20 07:03 EST 2014. Contains 252241 sequences.