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

1,4

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.

Links

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

Example

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],
    ...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A278885 A183049 A178086 * A281977 A240666 A052901

Adjacent sequences: A353293 A353294 A353295 * A353297 A353298 A353299

Keyword

nonn,base,tabf

Author

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

Status

approved