A118829 Denominators of the convergents of the 2-adic continued fraction of zero given by A118827.

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

Offset

1,2

Links

Table of n, a(n) for n=1..77.

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.

Example

For n>=1, convergents A118828(k)/A118829(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, ...

Prog

(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]}

Crossrefs

Cf. A118827 (partial quotients), A118829 (denominators).

Sequence in context: A165579 A130911 A319300 * A118832 A122807 A105700

Adjacent sequences: A118826 A118827 A118828 * A118830 A118831 A118832

Keyword

frac,sign

Author

Paul D. Hanna, May 01 2006

Status

approved