A332111 Numbers that are not the sum of eleven (11) positive cubes.

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

Offset

1,2

Comments

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

Example

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}.

Mathematica

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

Prog

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

Crossrefs

Complement of A003334.

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

Sequence in context: A328869 A004744 A171987 * A072226 A247809 A247802

Adjacent sequences: A332108 A332109 A332110 * A332112 A332113 A332114

Keyword

nonn,fini,full

Author

M. F. Hasler, Aug 25 2020

Status

approved