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

0,7

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Pages 61-62 of Matters Computational (The Fxtbook).

Formula

A184615(n) - a(n) = n

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

Example

(see A184615)

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 *)

Prog

(PARI) (see A184615)

Crossrefs

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

Sequence in context: A325774 A350488 A212868 * A261139 A065860 A363494

Adjacent sequences: A184613 A184614 A184615 * A184617 A184618 A184619

Keyword

nonn

Author

Joerg Arndt, Jan 18 2011

Status

approved