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A330271
a(n) is the least nonnegative integer k such that n XOR k is a cube (where XOR denotes the bitwise XOR operator).
3
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
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.
Sequence in context: A341948 A347661 A007730 * A257686 A057144 A198332
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 08 2019
STATUS
approved