cp's OEIS Frontend

A118832 Denominators of the convergents of the 2-adic continued fraction of zero given by A118830.

%I A118832 #4 Mar 30 2012 18:36:57
%S A118832 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 A118832 -31,-30,-1,-34,33,32,1,64,-63,-62,-1,-66,65,64,1,72,-71,-70,-1,-74,
%U A118832 73,72,1,88,-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,-170,169,168
%N A118832 Denominators of the convergents of the 2-adic continued fraction of zero given by A118830.
%F A118832 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 A118832 For n>=1, convergents A118831(k)/A118832(k) are:
%e A118832 at k = 4*n: 1/(2*A080277(n));
%e A118832 at k = 4*n+1: 1/(2*A080277(n)-1);
%e A118832 at k = 4*n+2: 1/(2*A080277(n)-2);
%e A118832 at k = 4*n-1: 0.
%e A118832 Convergents begin:
%e A118832 -1/1, -1/2, 0/-1, -1/-2, 1/1, 1/0, 0/1, 1/8,
%e A118832 -1/-7, -1/-6, 0/-1, -1/-10, 1/9, 1/8, 0/1, 1/24,
%e A118832 -1/-23, -1/-22, 0/-1, -1/-26, 1/25, 1/24, 0/1, 1/32,
%e A118832 -1/-31, -1/-30, 0/-1, -1/-34, 1/33, 1/32, 0/1, 1/64, ...
%o A118832 (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)[2,1]}
%Y A118832 Cf. A080277; A118830 (partial quotients), A118831 (numerators).
%K A118832 frac,sign
%O A118832 1,2
%A A118832 _Paul D. Hanna_, May 01 2006