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A118829 Denominators of the convergents of the 2-adic continued fraction of zero given by A118827. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 06:38 EDT 2019. Contains 323386 sequences. (Running on oeis4.)