A330271 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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