A085424 - OEIS

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

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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).