A353296 Pairs (i,j) of positive integers with at least one common 1-bit sorted first by i+j then by i.

1, 1, 1, 3, 2, 2, 3, 1, 2, 3, 3, 2, 1, 5, 3, 3, 5, 1, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 1, 9, 3, 7, 4, 6, 5, 5, 6, 4, 7, 3, 9, 1, 4, 7, 5, 6, 6, 5, 7, 4, 1, 11, 2, 10, 3, 9, 5, 7, 6, 6, 7, 5, 9, 3, 10, 2, 11, 1

Offset: 1

Author

Rémy Sigrist and N. J. A. Sloane, Apr 09 2022

Keywords

• nonn
• base
• tabf

Comments

Pairs (i,j) with AND(i,j) <> 0.

See A352909 for the other pairs.

There are A048967(n) pairs (i,j) with n = i+j.

Examples

			The first pairs are:
    [1, 1],
    [1, 3], [2, 2], [3, 1],
    [2, 3], [3, 2],
    [1, 5], [3, 3], [5, 1],
    [1, 7], [2, 6], [3, 5], [4, 4], [5, 3], [6, 2], [7, 1],
    [2, 7], [3, 6], [4, 5], [5, 4], [6, 3], [7, 2],
    [1, 9], [3, 7], [4, 6], [5, 5], [6, 4], [7, 3], [9, 1],
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..12392 (values for i+j <= 128)

Crossrefs

Cf. A004198, A048967, A352909, A353297 (i values), A353298 (j values).

Programs

Mathematica

A353296row[ij_] := Select[Array[{#, ij-#} &, ij], BitAnd @@ # > 0 &];
Array[A353296row, 15] (* Paolo Xausa, Feb 24 2024 *)

PARI

for (ij=1, 12, for (i=1, ij, j=ij-i; if (bitand(i,j), print1(i", "j", "))))