A332111

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

DATA

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, 30, 31, 33, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 61, 62, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 82, 83, 85, 87, 90, 92, 94, 97, 99

PYTHON IMPLEMENTATION

No Python implementation recorded in the local database yet.

PROGRAMS

Mathematica

Select[Range[400], (pr = PowersRepresentations[#, 11, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* adapted from _Amiram Eldar_'s code for A332110 *)

Other Programs

• (PARI) :

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

COMMENTS

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

EXAMPLES

• The smallest positive numbers not in the sequence are:
• 11 = 11 * 1^3, 18 = 2^3 + 10 * 1^3, 25 = 2 * 2^3 + 9 * 1^3,
• 32 = 3 * 2^3 + 8 * 1^3 and then 37 = 3^3 + 10 * 1^3.
• 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}.

LINKS

• M. F. Hasler, Table of n, a(n) for n = 1..92 (full sequence).
• Brennan Benfield and Oliver Lippard, Integers that are not the sum of positive powers, arXiv:2404.08193 [math.NT], 2024. See p. 4.

CROSSREFERENCES

• Complement of A003334.
• Cf. A332107, A332108, A332109, A332110 (analog for 7, 8, 9 and 10 cubes).
• See also the official entry at https://oeis.org/A332111

METADATA

• OFFSET : 1,2
• KEYWORDS : nonn,fini,full
• AUTHOR : M. F. Hasler, Aug 25 2020
• IDENTIFICATION : #12 Apr 18 2024 13:50:44