A046047 Sum of 16 but no fewer nonzero fourth powers.

31, 46, 61, 76, 111, 126, 141, 156, 191, 206, 221, 236, 271, 286, 301, 316, 351, 366, 381, 396, 431, 446, 461, 476, 496, 511, 526, 541, 556, 591, 606, 621, 671, 686, 701, 736, 751, 766, 781, 831, 846, 861, 911, 926, 941, 976, 991, 1006, 1021, 1071, 1086

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

What is the least k such that the sequence "Sum of k but no fewer nonzero fourth powers." is finite? - David A. Corneth, Jun 24 2018

13792 is the last number requiring 17 nonzero fourth powers. This sequence is infinite since numbers of the form 31*16^e always require 16 but no fewer. - Jianing Song, Jul 08 2018

Links

• David A. Corneth, Table of n, a(n) for n = 1..681 (terms <= 200000)
• Eric Weisstein's World of Mathematics, Biquadratic Number
• Wikipedia, Waring's problem

Crossrefs

Cf. A000583, A002377, A046046, A046048, A099591.

Programs

Mathematica

Select[Range[  1100], (pr = PowersRepresentations[#, 16, 4]; test = pr != {} && Count[pr, r_ /; (Times @@ r) == 0] == 0; If[test, Print[#]]; test) &] (* Jean-François Alcover, Oct 30 2012 *)

Extensions

More terms from Arlin Anderson (starship1(AT)gmail.com)