A118826 Denominators of the convergents of the 2-adic continued fraction of zero given by A118824.

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

1,8

Links

Table of n, a(n) for n=1..80.

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.

Example

For n>=1, convergents A118825(k)/A118826(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.
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, ...

Prog

(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]}

Crossrefs

Cf. A006519, A080277; A118824 (partial quotients), A118825 (numerators).

Sequence in context: A098233 A200602 A118823 * A330924 A165663 A254397

Adjacent sequences: A118823 A118824 A118825 * A118827 A118828 A118829

Keyword

frac,sign

Author

Paul D. Hanna, May 01 2006

Status

approved