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

Author

N. J. A. Sloane, Apr 09 2022

Keywords

• nonn
• tabf
• base
• look

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).

Examples

			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], ...
		

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.]

Crossrefs

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

Programs

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 *)