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A118831 Numerators of the convergents of the 2-adic continued fraction of zero given by A118830. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..107.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, -1).

FORMULA

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

a(n)=1/8*{2*(n mod 8)-[(n+1) mod 8]+[(n+2) mod 8]-2*[(n+4) mod 8]+[(n+5) mod 8]-[(n+6) mod 8]} with n>=0 - Paolo P. Lava, Nov 27 2006

a(n)=-a(n-4). - R. J. Mathar, Jul 22 2009

EXAMPLE

For n>=1, convergents A118831(k)/A118832(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. A118830 (partial quotients), A118832 (denominators).

Sequence in context: A188082 A046980 A152822 * A118828 A105234 A285599

Adjacent sequences:  A118828 A118829 A118830 * A118832 A118833 A118834

KEYWORD

frac,sign

AUTHOR

Paul D. Hanna, May 01 2006

EXTENSIONS

G.f. corrected by R. J. Mathar, Jul 22 2009

STATUS

approved

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Last modified May 24 11:23 EDT 2019. Contains 323529 sequences. (Running on oeis4.)