%I A118826
%S A118826 1,1,1,1,1,0,1,4,7,3,1,5,9,4,1,12,23,11,1,13,25,12,1,16,31,15,1,17,33,
               16,
%T A118826 1,32,63,31,1,33,65,32,1,36,71,35,1,37,73,36,1,44,87,43,1,45,89,44,1,48,
%U A118826 95,47,1,49,97,48,1,80,159,79,1,81,161,80,1,84,167,83,1,85,169,84,1,92
%V A118826 1,1,-1,-1,1,0,1,4,-7,-3,-1,-5,9,4,1,12,-23,-11,-1,-13,25,12,1,16,-31,
               -15,-1,-17,33,16,
%W A118826 1,32,-63,-31,-1,-33,65,32,1,36,-71,-35,-1,-37,73,36,1,44,-87,-43,-1,-45,
               89,44,1,48,
%X A118826 -95,-47,-1,-49,97,48,1,80,-159,-79,-1,-81,161,80,1,84,-167,-83,-1,-85,
               169,84,1,92
%N A118826 Denominators of the convergents of the 2-adic continued fraction of zero 
               given by A118824.
%F A118826 a(4*n) = (-1)^n*A080277(n); a(4*n+1) = -(-1)^n*(2*A080277(n)-1); a(4*n+2) 
               = -(-1)^n*(A080277(n)-1); a(4*n-1) = (-1)^n.
%e A118826 For n>=1, convergents A118825(k)/A118826(k) are:
%e A118826 at k = 4*n: 1/A080277(n);
%e A118826 at k = 4*n+1: 2/(2*A080277(n)-1);
%e A118826 at k = 4*n+2: 1/(A080277(n)-1);
%e A118826 at k = 4*n-1: 0.
%e A118826 Convergents begin:
%e A118826 -2/1, -1/1, 0/-1, -1/-1, 2/1, 1/0, 0/1, 1/4,
%e A118826 -2/-7, -1/-3, 0/-1, -1/-5, 2/9, 1/4, 0/1, 1/12,
%e A118826 -2/-23, -1/-11, 0/-1, -1/-13, 2/25, 1/12, 0/1, 1/16,
%e A118826 -2/-31, -1/-15, 0/-1, -1/-17, 2/33, 1/16, 0/1, 1/32, ...
%o A118826 (PARI) {a(n)=local(p=-2,q=+1,v=vector(n,i,if(i%2==1,p,q*2^valuation(i/
               2,2)))); contfracpnqn(v)[2,1]}
%Y A118826 Cf. A006519, A080277; A118824 (partial quotients), A118825 (numerators).
%Y A118826 Sequence in context: A076414 A098233 A118823 this_sequence A165663 A100127 
               A130204
%Y A118826 Adjacent sequences: A118823 A118824 A118825 this_sequence A118827 A118828 
               A118829
%K A118826 frac,sign
%O A118826 1,8
%A A118826 Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2006