A046047 - OEIS

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, 1101, 1151

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OFFSET

1,1

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

REFERENCES

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

LINKS

Martin Fuller, Table of n, a(n) for n = 1..2983 (terms <= 10^13) (first 681 terms <= 200000 from David A. Corneth)

Martin Fuller, C++ program

Eric Weisstein's World of Mathematics, Biquadratic Number

Wikipedia, Waring's problem

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 *)

PROG

(C++) // See Fuller link.

CROSSREFS

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

Sequence in context: A033905 A033661 A219243 * A014313 A095318 A130096

Adjacent sequences: A046044 A046045 A046046 * A046048 A046049 A046050

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved