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

Author

Rémy Sigrist, Dec 08 2019

Keywords

• nonn
• base

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

Crossrefs

See A330271 for the XOR variant.

Cf. A000225, A000578, A003986.

Programs

Mathematica

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

PARI

See Links section.

Formula

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

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