cp's OEIS Frontend

A118831 Numerators of the convergents of the 2-adic continued fraction of zero given by A118830.

%I A118831 #20 Dec 14 2023 05:24:20
%S A118831 -1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,
%T A118831 1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,
%U A118831 -1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0,-1,1,1,0,1,-1,-1,0
%N A118831 Numerators of the convergents of the 2-adic continued fraction of zero given by A118830.
%H A118831 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,-1).
%F A118831 Period 8 sequence: [ -1,-1,0,-1,1,1,0,1].
%F A118831 G.f.: -x*(1+x+x^3)/(1+x^4). [corrected by _R. J. Mathar_, Jul 22 2009]
%F A118831 a(n) = -a(n-4). - _R. J. Mathar_, Jul 22 2009
%e A118831 For n>=1, convergents A118831(k)/A118832(k) are:
%e A118831 at k = 4*n: 1/(2*A080277(n));
%e A118831 at k = 4*n+1: 1/(2*A080277(n)-1);
%e A118831 at k = 4*n+2: 1/(2*A080277(n)-2);
%e A118831 at k = 4*n-1: 0.
%e A118831 Convergents begin:
%e A118831 -1/1, -1/2, 0/-1, -1/-2, 1/1, 1/0, 0/1, 1/8,
%e A118831 -1/-7, -1/-6, 0/-1, -1/-10, 1/9, 1/8, 0/1, 1/24,
%e A118831 -1/-23, -1/-22, 0/-1, -1/-26, 1/25, 1/24, 0/1, 1/32,
%e A118831 -1/-31, -1/-30, 0/-1, -1/-34, 1/33, 1/32, 0/1, 1/64, ...
%o A118831 (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 A118831 Cf. A118830 (partial quotients), A118832 (denominators).
%K A118831 frac,sign
%O A118831 1,1
%A A118831 _Paul D. Hanna_, May 01 2006