This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287286 #31 Dec 18 2023 08:25:59
%S A287286 1,4,4,15,5,9,4,32,13,12,11,16,6,14,15,64,6,27,4,25,24,23,23,32,10,26,
%T A287286 40,29,29,31,5,128,33,10,35,37,9,9,39,41,41,49,12,44,15,47,10,64,13,
%U A287286 62,51,53,53,81,60,56,14,59,5,61,11,12,63,256,65,67,12,68,69,71,6,73,16,74,75,16,14,84
%N A287286 a(n) = smallest integer s such that every element of the ring of integers mod t for any t can be written as a sum of s n-th powers.
%C A287286 One needs only check a finite number of values (depending on the power).
%C A287286 See Small's paper in references for precise quantitive information.
%C A287286 a(2) <= 4 follows from Lagrange's four squares theorem.
%C A287286 Differs from A040004 only at k=4. - _Andrey Zabolotskiy_, Jun 03 2017
%D A287286 G. H. Hardy and J. E. Littlewood, Some Problems of "Partitio Numerorum" (VIII): The Number Gamma(k) in Waring's Problem, Proc London Math Soc. 28 (1928), 518--542. [G. H. Hardy, Collected Papers. Vols. 1-, Oxford Univ. Press, 1966-; see vol. 1, pp. 406-530.]
%D A287286 Wladyslaw Narkiewicz, Rational Number Theory in the 20th Century: From PNT to FLT, Springer Science & Business Media, 2011, pages 154-155.
%H A287286 H. Sekigawa and K. Koyama, <a href="https://doi.org/10.1090/S0025-5718-99-01067-4">Nonexistence Conditions of a Solution for the congruence x_1^k + ... + x_s^k = N (mod p^n)</a>, Math. Comp. 68 (1999), 1283--1297.
%H A287286 C. Small, <a href="http://www.jstor.org/stable/2318299">Waring's problem mod n</a>, Amer. Math. Monthly 84 (1977), no. 1, 12--25.
%H A287286 R. C. Vaughan and T. D. Wooley, <a href="https://personal.science.psu.edu/rcv4/Waring.pdf">Waring’s problem: a survey</a>, Number Theory for the Millennium, III (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, pp. 301-340.
%e A287286 a(3) <= 4 states that every element of every ring of integers mod m can be written as a sum of 4 (or fewer) cubes. a(3) >= 4, since in Z/9Z, the cubes are {0,1,8} so that 4 is not the sum of any three cubes in Z/9Z. Hence a(3) = 4.
%Y A287286 Cf. A079611, A174406, A040004.
%K A287286 nonn
%O A287286 1,2
%A A287286 _David Covert_, May 22 2017
%E A287286 Edited by _Andrey Zabolotskiy_, Jun 10 2017