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

0,3

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

See A330270 for the square variant.

See A330272 for the OR variant.

Cf. A000578, A003987, A296615.

Sequence in context: A341948 A347661 A007730 * A257686 A057144 A198332

Adjacent sequences: A330268 A330269 A330270 * A330272 A330273 A330274

Keyword

nonn,base

Author

Rémy Sigrist, Dec 08 2019

Status

approved