A085425 Number of minus 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).

0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 1

Offset: 1

Author

Ralf Stephan, Jun 30 2003

Keywords

• nonn
• easy
• base

Links

• 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), A085424 (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)) ;