A046050 Sum of 19 but no fewer nonzero fourth powers.

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

Offset

1,1

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.

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 310.

Links

Table of n, a(n) for n=1..7.

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.

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 *)

Prog

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

Crossrefs

Cf. A000583, A002377, A046049.

Sequence in context: A031890 A140008 A142159 * A044330 A044711 A362360

Adjacent sequences: A046047 A046048 A046049 * A046051 A046052 A046053

Keyword

nonn,fini,full

Author

Eric W. Weisstein

Extensions

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

Status

approved