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A118828 Numerators of the convergents of the 2-adic continued fraction of zero given by A118827. 4
1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..108.

FORMULA

Period 8 sequence: [1,-1,0,-1,-1,1,0,1]. G.f.: (1-x-x^3)/(1+x^4).

a(n)=1/8*{-[(n+1) mod 8]+[(n+2) mod 8]-2*[(n+3) mod 8]+[(n+5) mod 8]-[(n+6) mod 8]+2*[(n+7) mod 8]} with n>=0 - Paolo P. Lava, Nov 27 2006

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/(-1)^n.

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: A046980 A152822 A118831 * A105234 A285599 A284386

Adjacent sequences:  A118825 A118826 A118827 * A118829 A118830 A118831

KEYWORD

frac,sign

AUTHOR

Paul D. Hanna, May 01 2006

STATUS

approved

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)