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A118827 2-adic continued fraction of zero, where a(n) = 1 if n is odd, otherwise -2*A006519(n/2). 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, A118830. A006519(n) is the highest power of 2 dividing n; A080277 = partial sums of A038712, where A038712(n) = 2*A006519(n) - 1.

Multiplicative because both A006519 and A165326 are. - Andrew Howroyd, Aug 01 2018

LINKS

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

FORMULA

a(n) = A165326(n) * A006519(n). - Andrew Howroyd, Aug 01 2018

EXAMPLE

For n >= 1, convergents A118828(k)/A118829(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*2^(IntegerExponent[#, 2] - 1)] &, 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: A118828/A118829; variants: A118821, A118824, A118830; A100338, A165326.

Sequence in context: A084236 A068057 A003484 * A118830 A055975 A006519

Adjacent sequences:  A118824 A118825 A118826 * A118828 A118829 A118830

KEYWORD

cofr,sign,mult

AUTHOR

Paul D. Hanna, May 01 2006

STATUS

approved

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Last modified April 19 10:38 EDT 2019. Contains 322255 sequences. (Running on oeis4.)