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Search: id:A118821
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| A118821 |
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2-adic continued fraction of zero, where a(n) = if n=1(mod 2), +2, else -1*A006519(n/2). |
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+0
6
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Limit of convergents equals zero; only the 6-th 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.
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EXAMPLE
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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, ...
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PROGRAM
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(PARI) a(n)=local(p=+2, q=-1); if(n%2==1, p, q*2^valuation(n/2, 2))
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CROSSREFS
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Cf. A006519, A080277; convergents: A118822/A118823; variants: A118824, A118827, A118830; A100338.
Sequence in context: A007302 A099910 A043555 this_sequence A118824 A082641 A138553
Adjacent sequences: A118818 A118819 A118820 this_sequence A118822 A118823 A118824
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KEYWORD
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cofr,sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2006
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