cp's OEIS Frontend

A184616 Negated negative parts of the nonadjacent forms.

%I A184616 #22 Feb 25 2023 04:27:54
%S A184616 0,0,0,1,0,0,2,1,0,0,0,5,4,4,2,1,0,0,0,1,0,0,10,9,8,8,8,5,4,4,2,1,0,0,
%T A184616 0,1,0,0,2,1,0,0,0,21,20,20,18,17,16,16,16,17,16,16,10,9,8,8,8,5,4,4,
%U A184616 2,1,0,0,0,1,0,0,2,1,0,0,0,5,4,4,2,1,0,0,0,1,0,0,42,41
%N A184616 Negated negative parts of the nonadjacent forms.
%C A184616 This sequence together with A184615 (positive parts) gives the (signed binary) nonadjacent form (NAF) of n, see fxtbook link and example in A184615.
%C A184616 No two adjacent bits in the binary representations of a(n) are 1.
%C A184616 No two adjacent bits in the binary representations of a(n)+A184615(n) are 1.
%H A184616 Rémy Sigrist, <a href="/A184616/b184616.txt">Table of n, a(n) for n = 0..8192</a>
%H A184616 Pages 61-62 of <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>.
%F A184616 A184615(n) - a(n) = n
%F A184616 a(n) + A184615(n) = A184617(n)
%e A184616 (see A184615)
%t A184616 bin2naf[x_] := Module[{xh, x3, c, np, nm},
%t A184616   xh = BitShiftRight[x, 1];
%t A184616   x3 = x + xh;
%t A184616   c = BitXor[xh, x3];
%t A184616   np = BitAnd[x3, c];
%t A184616   nm = BitAnd[xh, c];
%t A184616   Return[{np, nm}]];
%t A184616 a[n_] := bin2naf[n][[2]];
%t A184616 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 30 2019, from PARI code in A184615 *)
%o A184616 (PARI) (see A184615)
%Y A184616 Cf. A184615 (positive parts), A184617 (sums of both parts =A184615+A184616).
%K A184616 nonn
%O A184616 0,7
%A A184616 _Joerg Arndt_, Jan 18 2011