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A118830 2-adic continued fraction of zero, where a(n) = -1 if n is odd, 2*A006519(n/2) otherwise. 6
-1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 32, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 64, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 32, -1, 2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limit of convergents equals zero; only the 6th convergent is indeterminate. Other 2-adic continued fractions of zero are: A118821, A118824, A118827. A006519(n) is the highest power of 2 dividing n; A080277 = partial sums of A038712, where A038712(n) = 2*A006519(n) - 1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

For n >= 1, convergents A118831(k)/A118832(k):

  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, ...

MATHEMATICA

Array[If[OddQ@ #, -1, 2^IntegerExponent[#, 2]] &, 99] (* Michael De Vlieger, Nov 06 2018 *)

PROG

(PARI) a(n)=local(p=-1, q=+2); if(n%2==1, p, q*2^valuation(n/2, 2))

CROSSREFS

Cf. A006519, A080277; convergents: A118831/A118832; variants: A118821, A118824, A118827; A100338.

Sequence in context: A068057 A003484 A118827 * A055975 A006519 A322362

Adjacent sequences:  A118827 A118828 A118829 * A118831 A118832 A118833

KEYWORD

cofr,sign

AUTHOR

Paul D. Hanna, May 01 2006

STATUS

approved

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Last modified April 24 04:21 EDT 2019. Contains 322406 sequences. (Running on oeis4.)