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%I #22 Jan 23 2014 08:24:22
%S 79,159,239,319,399,479,559
%N Sum of 19 but no fewer nonzero fourth powers.
%C Dickson noted that this sequence is complete to 4100. Deshouillers, Hennecart and Landreau showed that this sequence is complete up to 10^245, and Kawada, Wooley and Deshouillers showed that it is complete beyond 10^220.
%D J.-M. Deshouillers, K. Kawada and T. D. Wooley, On sums of sixteen biquadrates, Mem. Soc. Math. Fr. 100 (2005), pp. 120.
%H J.-M. Deshouillers, F. Hennecart and B. Landreau, <a href="http://archive.numdam.org/article/JTNB_2000__12_2_411_0.pdf">Waring's Problem for sixteen biquadrates - numerical results</a>, Journal de Théorie des Nombres de Bordeaux 12:2 (2000), pp. 411-422.
%H L. E. Dickson, <a href="http://www.ams.org/journals/bull/1933-39-10/S0002-9904-1933-05719-1/S0002-9904-1933-05719-1.pdf">Recent progress on Waring's theorem and its generalizations</a>, Bull. Amer. Math. Soc. 39:10 (1933), pp. 701-727.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%t Select[Range[1000], (pr = PowersRepresentations[#, 19, 4]; test = pr != {} && FreeQ[pr, r_List /; (Times @@ r) == 0]; If[test, Print[#]]; test) &] (* _Jean-François Alcover_, Oct 30 2012 *)
%o (PARI) is(n)=n%80==79 && n<600 && n>0 \\ _Charles R Greathouse IV_, Jan 23 2014
%Y Cf. A000583, A002377, A046049.
%K nonn,fini,full
%O 1,1
%A _Eric W. Weisstein_
%E More terms from Arlin Anderson (starship1(AT)gmail.com). _Jud McCranie_ remarks that probably all terms are shown.
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