login
A184616
Negated negative parts of the nonadjacent forms.
6
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.
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 18 2011
STATUS
approved