|
%I #4 Mar 30 2012 18:36:57
%S 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,
%T -15,-1,-17,33,16,1,32,-63,-31,-1,-33,65,32,1,36,-71,-35,-1,-37,73,36,
%U 1,44,-87,-43,-1,-45,89,44,1,48,-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 Denominators of the convergents of the 2-adic continued fraction of zero given by A118824.
%F 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 For n>=1, convergents A118825(k)/A118826(k) are:
%e at k = 4*n: 1/A080277(n);
%e at k = 4*n+1: 2/(2*A080277(n)-1);
%e at k = 4*n+2: 1/(A080277(n)-1);
%e at k = 4*n-1: 0.
%e Convergents begin:
%e -2/1, -1/1, 0/-1, -1/-1, 2/1, 1/0, 0/1, 1/4,
%e -2/-7, -1/-3, 0/-1, -1/-5, 2/9, 1/4, 0/1, 1/12,
%e -2/-23, -1/-11, 0/-1, -1/-13, 2/25, 1/12, 0/1, 1/16,
%e -2/-31, -1/-15, 0/-1, -1/-17, 2/33, 1/16, 0/1, 1/32, ...
%o (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 Cf. A006519, A080277; A118824 (partial quotients), A118825 (numerators).
%K frac,sign
%O 1,8
%A _Paul D. Hanna_, May 01 2006
|
