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

1, 2, -1, -2, 1, 0, 1, 8, -7, -6, -1, -10, 9, 8, 1, 24, -23, -22, -1, -26, 25, 24, 1, 32, -31, -30, -1, -34, 33, 32, 1, 64, -63, -62, -1, -66, 65, 64, 1, 72, -71, -70, -1, -74, 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

Offset: 1

Author

Paul D. Hanna, May 01 2006

Keywords

• frac
• sign

Examples

			For n>=1, convergents A118831(k)/A118832(k) are:
at k = 4*n: 1/(2*A080277(n));
at k = 4*n+1: 1/(2*A080277(n)-1);
at k = 4*n+2: 1/(2*A080277(n)-2);
at k = 4*n-1: 0.
Convergents begin:
-1/1, -1/2, 0/-1, -1/-2, 1/1, 1/0, 0/1, 1/8,
-1/-7, -1/-6, 0/-1, -1/-10, 1/9, 1/8, 0/1, 1/24,
-1/-23, -1/-22, 0/-1, -1/-26, 1/25, 1/24, 0/1, 1/32,
-1/-31, -1/-30, 0/-1, -1/-34, 1/33, 1/32, 0/1, 1/64, ...
		

Crossrefs

Cf. A080277; A118830 (partial quotients), A118831 (numerators).

Programs

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]}

Formula

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.