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

Author

Ralf Stephan, Jun 30 2003

Keywords

• nonn
• easy
• base

Links

• 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.

Crossrefs

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

Programs

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)) ;