A046050 Sum of 19 but no fewer nonzero fourth powers.

79, 159, 239, 319, 399, 479, 559

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini
• full

Comments

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.

References

• J.-M. Deshouillers, K. Kawada and T. D. Wooley, On sums of sixteen biquadrates, Mem. Soc. Math. Fr. 100 (2005), pp. 120.

Links

• J.-M. Deshouillers, F. Hennecart and B. Landreau, Waring's Problem for sixteen biquadrates - numerical results, Journal de Théorie des Nombres de Bordeaux 12:2 (2000), pp. 411-422.
• L. E. Dickson, Recent progress on Waring's theorem and its generalizations, Bull. Amer. Math. Soc. 39:10 (1933), pp. 701-727.
• Tanya Khovanova, Non Recursions
• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

Cf. A000583, A002377, A046049.

Programs

Mathematica

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 *)

PARI

is(n)=n%80==79 && n<600 && n>0 \\ Charles R Greathouse IV, Jan 23 2014

Extensions

More terms from Arlin Anderson (starship1(AT)gmail.com). Jud McCranie remarks that probably all terms are shown.