A330272 a(n) is the least nonnegative integer k such that n OR k is a cube (where OR denotes the bitwise OR operator).

0, 0, 25, 24, 121, 120, 337, 336, 0, 18, 17, 16, 113, 112, 3361, 3360, 11, 10, 9, 8, 105, 104, 321, 320, 3, 2, 1, 0, 97, 96, 29761, 29760, 93, 92, 1297, 1296, 89, 88, 3337, 3336, 85, 84, 3333, 3332, 81, 80, 3329, 3328, 77, 76, 1281, 1280, 73, 72, 59265, 59264

Offset

0,3

Comments

The sequence is well defined:

- for any k >= 0, the binary expansion of m = A000225(k)^3 has k trailing 1's,

- hence for any n < 2^k, n OR m = m, which is a cube, QED.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, PARI program for A330272

Rémy Sigrist, Scatterplot of (x, y) such that x OR y is a cube, 0 <= x, y <= 1023

Formula

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

a(n) AND n = 0 (where AND denotes the bitwise AND operator).

Mathematica

A330272[n_] := Module[{k = -1}, While[!IntegerQ[CubeRoot[BitOr[n, ++k]]]]; k];
Array[A330272, 60, 0] (* Paolo Xausa, Feb 20 2024 *)

Prog

(PARI) See Links section.

Crossrefs

See A330271 for the XOR variant.

Cf. A000225, A000578, A003986.

Sequence in context: A022981 A023467 A158501 * A194219 A291434 A291476

Adjacent sequences: A330269 A330270 A330271 * A330273 A330274 A330275

Keyword

nonn,base

Author

Rémy Sigrist, Dec 08 2019

Status

approved