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A118821 2-adic continued fraction of zero, where a(n) = 2 if n is odd, -A006519(n/2) otherwise. 6
2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -8, 2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -16, 2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -8, 2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -32, 2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -8, 2, -1, 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -1, 2, -16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Limit of convergents equals zero; only the 6th convergent is indeterminate. Other 2-adic continued fractions of zero are A118824, A118827, A118830. 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 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, ...

MATHEMATICA

Array[-2^(IntegerExponent[#, 2] - 1) /. -1/2 -> 2 &, 96] (* Michael De Vlieger, Nov 02 2018 *)

PROG

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

CROSSREFS

Cf. A006519, A080277; convergents: A118822/A118823; variants: A118824, A118827, A118830; A100338.

Sequence in context: A043555 A242753 A232443 * A118824 A209402 A082641

Adjacent sequences:  A118818 A118819 A118820 * A118822 A118823 A118824

KEYWORD

cofr,sign

AUTHOR

Paul D. Hanna, May 01 2006

STATUS

approved

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Last modified May 21 00:51 EDT 2019. Contains 323428 sequences. (Running on oeis4.)