A118823 Denominators of the convergents of the 2-adic continued fraction of zero given by A118821.

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, 15, -1, 17, 33, -16, 1, -32, -63, 31, -1, 33, 65, -32, 1, -36, -71, 35, -1, 37, 73, -36, 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

Offset: 1

Author

Paul D. Hanna, May 01 2006

Keywords

• frac
• sign

Examples

			For n>=1, convergents A118822(k)/A118823(k) are:
at k = 4*n: -1/A080277(n);
at k = 4*n+1: -2/(2*A080277(n)-1);
at k = 4*n+2: -1/(A080277(n)-1);
at k = 4*n-1: 0/(-1)^n.
Convergents begin:
2/1, -1/-1, 0/-1, -1/1, -2/1, 1/0, 0/1, 1/-4,
2/-7, -1/3, 0/-1, -1/5, -2/9, 1/-4, 0/1, 1/-12,
2/-23, -1/11, 0/-1, -1/13, -2/25, 1/-12, 0/1, 1/-16,
2/-31, -1/15, 0/-1, -1/17, -2/33, 1/-16, 0/1, 1/-32, ...
		

Crossrefs

Cf. A080277; A118821 (partial quotients), A118822 (numerators).

Programs

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]}

Formula

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.