A330271 a(n) is the least nonnegative integer k such that n XOR k is a cube (where XOR denotes the bitwise XOR operator).

0, 0, 2, 2, 4, 4, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 11, 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4, 32, 32, 34, 34, 36, 36, 38, 38, 32, 33, 34, 35, 36, 37, 38, 39, 43, 42, 41, 40, 47, 46, 45, 44, 35, 34, 33, 32, 39, 38, 37, 36, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 0

Author

Rémy Sigrist, Dec 08 2019

Keywords

• nonn
• base

Examples

			For n = 4:
- 4 XOR 0 = 4 (not a cube),
- 4 XOR 1 = 5 (not a cube),
- 4 XOR 2 = 6 (not a cube),
- 4 XOR 3 = 7 (not a cube),
- 4 XOR 4 = 0 = 0^3,
- hence a(4) = 4.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Scatterplot of the ordinal transform of the first 2^20 terms
• Rémy Sigrist, Scatterplot of (x, y) such that x XOR y is a cube, 0 <= x, y <= 1023

Crossrefs

See A330270 for the square variant.

See A330272 for the OR variant.

Cf. A000578, A003987, A296615.

Programs

Mathematica

A330271[n_] := Module[{k = -1}, While[!IntegerQ[CubeRoot[BitXor[n, ++k]]]]; k];
Array[A330271, 100, 0] (* Paolo Xausa, Feb 20 2024 *)

PARI

a(n) = for (k=0, oo, if (ispower(bitxor(n,k),3), return (k)))

Python

from itertools import count
from sympy import integer_nthroot
def A330271(n): return next(k for k in count(0) if integer_nthroot(n^k,3)[1]) # Chai Wah Wu, Aug 23 2023

Formula

a(n) = 0 iff n is a cube.