A184616 Negated negative parts of the nonadjacent forms.

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, 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, 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

Offset: 0

Author

Joerg Arndt, Jan 18 2011

Keywords

• nonn

Comments

This sequence together with A184615 (positive parts) gives the (signed binary) nonadjacent form (NAF) of n, see fxtbook link and example in A184615.

No two adjacent bits in the binary representations of a(n) are 1.

No two adjacent bits in the binary representations of a(n)+A184615(n) are 1.

Examples

			(see A184615)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Pages 61-62 of Matters Computational (The Fxtbook).

Crossrefs

Cf. A184615 (positive parts), A184617 (sums of both parts =A184615+A184616).

Programs

Mathematica

bin2naf[x_] := Module[{xh, x3, c, np, nm},
  xh = BitShiftRight[x, 1];
  x3 = x + xh;
  c = BitXor[xh, x3];
  np = BitAnd[x3, c];
  nm = BitAnd[xh, c];
  Return[{np, nm}]];
a[n_] := bin2naf[n][[2]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 30 2019, from PARI code in A184615 *)

PARI

(see A184615)

Formula

A184615(n) - a(n) = n

a(n) + A184615(n) = A184617(n)