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Search: id:A118827
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| A118827 |
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2-adic continued fraction of zero, where a(n) = if n=1(mod 2), +1, else -2*A006519(n/2). |
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+0
6
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| 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; listen)
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OFFSET
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1,2
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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: 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.
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EXAMPLE
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For n>=1, convergents A118828(k)/A118829(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, ...
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PROGRAM
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(PARI) a(n)=local(p=+1, q=-2); if(n%2==1, p, q*2^valuation(n/2, 2))
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CROSSREFS
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Cf. A006519, A080277; convergents: A118828/A118829; variants: A118821, A118824, A118830; A100338.
Sequence in context: A003484 A006519 A055975 this_sequence A118830 A087258 A076775
Adjacent sequences: A118824 A118825 A118826 this_sequence A118828 A118829 A118830
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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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