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

%I A352909 #26 Feb 25 2024 06:00:38
%S A352909 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,
%T A352909 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,
%U A352909 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
%N A352909 Pairs (i,j) of nonnegative integers with disjoint binary expansions sorted first by i+j then by i.
%C A352909 Pairs (i,j) with AND(i,j) = 0.
%C A352909 _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).
%H A352909 N. J. A. Sloane, <a href="/A352909/b352909.txt">Table of n, a(n) for n = 1..4374</a>
%H A352909 N. J. A. Sloane, <a href="/A352909/a352909.txt">List of the 2187 pairs (i,j) with i+j <= 127</a>. [Note this is not a b-file.]
%e A352909 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], ...
%p A352909 with(Bits);
%p A352909 M:=16; Nlis:=[];
%p A352909 for s from 0 to M do for i from 0 to s do j:=s-i;
%p A352909 if And(i,j)=0 then Nlis:=[op(Nlis),[i,j]]; fi;
%p A352909 od: od:
%p A352909 Nlis;
%t A352909 A352909list[ij_] := Select[Array[{#, ij-#} &, ij+1, 0], BitAnd @@ # == 0 &];
%t A352909 Flatten[Array[A352909list, 15, 0]] (* _Paolo Xausa_, Feb 24 2024 *)
%Y A352909 Cf. A047999, A295989 (i values), A352910 (j values).
%K A352909 nonn,tabf,base,look
%O A352909 1,8
%A A352909 _N. J. A. Sloane_, Apr 09 2022