cp's OEIS Frontend

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).

%I A085424 #25 May 11 2018 03:08:06
%S A085424 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,
%T A085424 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,
%U A085424 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
%N 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).
%H A085424 Wieb Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.
%H A085424 C. Heuberger and H. Prodinger, <a href="http://dx.doi.org/10.1007/s006070170021">On minimal expansions in redundant number systems: Algorithms and quantitative analysis</a>, Computing 66(2001), 377-393.
%o A085424 (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);
%o A085424 a(n)=sum(r=0, log(3*n)\log(2)-1, (ep(r, n) == 1)) ;
%Y A085424 Cf. A005578, A085423, A007302 (nonzeros), A057526 (0's), A085425 (-1's).
%K A085424 nonn,easy,base
%O A085424 1,5
%A A085424 _Ralf Stephan_, Jun 30 2003