A352909 Pairs (i,j) of nonnegative integers with disjoint binary expansions sorted first by i+j then by i.

0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 4, 4, 0, 0, 5, 1, 4, 4, 1, 5, 0, 0, 6, 2, 4, 4, 2, 6, 0, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 0, 8, 8, 0, 0, 9, 1, 8, 8, 1, 9, 0, 0, 10, 2, 8, 8, 2, 10, 0, 0, 11, 1, 10, 2, 9, 3, 8, 8, 3, 9, 2, 10, 1, 11, 0, 0, 12, 4, 8, 8, 4, 12, 0, 0, 13, 1, 12, 4, 9, 5, 8, 8, 5, 9, 4, 12, 1, 13, 0

Offset

1,8

Comments

Pairs (i,j) with AND(i,j) = 0.

Allan C. Wechsler points out that when these points are plotted on a two-dimensional grid they form a rotated version of the Sierpinski Gasket (A047999).

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..4374

N. J. A. Sloane, List of the 2187 pairs (i,j) with i+j <= 127. [Note this is not a b-file.]

Example

The first few pairs are [0, 0], [0, 1], [1, 0], [0, 2], [2, 0], [0, 3], [1, 2], [2, 1], [3, 0], [0, 4], [4, 0], [0, 5], [1, 4], [4, 1], [5, 0], [0, 6], [2, 4], [4, 2], [6, 0], [0, 7], [1, 6], [2, 5], [3, 4], [4, 3], [5, 2], [6, 1], [7, 0], ...

Maple

with(Bits);
M:=16; Nlis:=[];
for s from 0 to M do for i from 0 to s do j:=s-i;
if And(i, j)=0 then Nlis:=[op(Nlis), [i, j]]; fi;
od: od:
Nlis;

Mathematica

A352909list[ij_] := Select[Array[{#, ij-#} &, ij+1, 0], BitAnd @@ # == 0 &];
Flatten[Array[A352909list, 15, 0]] (* Paolo Xausa, Feb 24 2024 *)

Crossrefs

Cf. A047999, A295989 (i values), A352910 (j values).

Sequence in context: A357019 A352562 A362326 * A323473 A341288 A325820

Adjacent sequences: A352906 A352907 A352908 * A352910 A352911 A352912

Keyword

nonn,tabf,base,look

Author

N. J. A. Sloane, Apr 09 2022

Status

approved