A085424 Number of ones in the symmetric signed digit expansion of n with q=2 (i.e., the representation of n in the (-1,0,1)_2 number system).

1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1

Offset

1,5

Links

Table of n, a(n) for n=1..96.

Wieb Bosma, Signed bits and fast exponentiation, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.

C. Heuberger and H. Prodinger, On minimal expansions in redundant number systems: Algorithms and quantitative analysis, Computing 66(2001), 377-393.

Prog

(PARI) ep(r, n)=local(t=n/2^(r+2)); floor(t+5/6)-floor(t+4/6)-floor(t+2/6)+floor(t+1/6);
a(n)=sum(r=0, log(3*n)\log(2)-1, (ep(r, n) == 1)) ;

Crossrefs

Cf. A005578, A085423, A007302 (nonzeros), A057526 (0's), A085425 (-1's).

Sequence in context: A358260 A368978 A255326 * A088737 A318434 A321455

Adjacent sequences: A085421 A085422 A085423 * A085425 A085426 A085427

Keyword

nonn,easy,base

Author

Ralf Stephan, Jun 30 2003

Status

approved