A118829 - OEIS

%I #4 Mar 30 2012 18:36:57

%S 1,-2,-1,2,1,0,1,-8,-7,6,-1,10,9,-8,1,-24,-23,22,-1,26,25,-24,1,-32,

%T -31,30,-1,34,33,-32,1,-64,-63,62,-1,66,65,-64,1,-72,-71,70,-1,74,73,

%U -72,1,-88,-87,86,-1,90,89,-88,1,-96,-95,94,-1,98,97,-96,1,-160,-159,158,-1,162,161,-160,1,-168,-167,166,-1,170,169

%N Denominators of the convergents of the 2-adic continued fraction of zero given by A118827.

%F a(4*n) = -(-1)^n*2*A080277(n); a(4*n+1) = -(-1)^n*(2*A080277(n)-1); a(4*n+2) = (-1)^n*(2*A080277(n)-2); a(4*n-1) = (-1)^n.

%e For n>=1, convergents A118828(k)/A118829(k) are:

%e at k = 4*n: -1/(2*A080277(n));

%e at k = 4*n+1: -1/(2*A080277(n)-1);

%e at k = 4*n+2: -1/(2*A080277(n)-2);

%e at k = 4*n-1: 0.

%e Convergents begin:

%e 1/1, -1/-2, 0/-1, -1/2, -1/1, 1/0, 0/1, 1/-8,

%e 1/-7, -1/6, 0/-1, -1/10, -1/9, 1/-8, 0/1, 1/-24,

%e 1/-23, -1/22, 0/-1, -1/26, -1/25, 1/-24, 0/1, 1/-32,

%e 1/-31, -1/30, 0/-1, -1/34, -1/33, 1/-32, 0/1, 1/-64, ...

%o (PARI) {a(n)=local(p=+1,q=-2,v=vector(n,i,if(i%2==1,p,q*2^valuation(i/2,2)))); contfracpnqn(v)[1,1]}

%Y Cf. A118827 (partial quotients), A118829 (denominators).

%K frac,sign

%O 1,2

%A _Paul D. Hanna_, May 01 2006