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A118823 Denominators of the convergents of the 2-adic continued fraction of zero given by A118821. 3
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 (list; graph; refs; listen; history; text; internal format)
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 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, ...

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

Sequence in context: A198574 A098233 A200602 * A118826 A165663 A254397

Adjacent sequences:  A118820 A118821 A118822 * A118824 A118825 A118826

KEYWORD

frac,sign

AUTHOR

Paul D. Hanna, May 01 2006

STATUS

approved

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Last modified June 19 16:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)