A332111 - OEIS

%I #12 Apr 18 2024 13:50:44

%S 1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,19,20,21,22,23,24,26,27,28,29,

%T 30,31,33,34,35,36,38,40,41,42,43,45,47,48,49,50,52,54,55,56,57,59,61,

%U 62,64,66,68,69,71,73,75,76,78,80,82,83,85,87,90,92,94,97,99

%N Numbers that are not the sum of eleven (11) positive cubes.

%C The sequence is finite, with last term a(92) = 321.

%H M. F. Hasler, <a href="/A332111/b332111.txt">Table of n, a(n) for n = 1..92</a> (full sequence).

%H Brennan Benfield and Oliver Lippard, <a href="https://arxiv.org/abs/2404.08193">Integers that are not the sum of positive powers</a>, arXiv:2404.08193 [math.NT], 2024. See p. 4.

%e The smallest positive numbers not in the sequence are:

%e   11 = 11 * 1^3, 18 = 2^3 + 10 * 1^3, 25 = 2 * 2^3 + 9 * 1^3,

%e   32 = 3 * 2^3 + 8 * 1^3 and then 37 = 3^3 + 10 * 1^3.

%e The last 23 terms of the sequence (not in the data section) are a(70 .. 92) = {101, 104, 106, 108, 111, 113, 118, 120, 125, 127, 132, 134, 139, 146, 153, 160, 171, 190, 197, 209, 216, 223, 321}.

%t Select[Range[400], (pr = PowersRepresentations[#, 11, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* adapted from _Amiram Eldar_'s code for A332110 *)

%o (PARI) A332111=setminus([1..333],A003333_upto(444))

%Y Complement of A003334.

%Y Cf. A332107, A332108, A332109, A332110 (analog for 7, 8, 9 and 10 cubes).

%K nonn,fini,full

%O 1,2

%A _M. F. Hasler_, Aug 25 2020