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Search: id:A118830
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| A118830 |
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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, A118827. 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 A118831(k)/A118832(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: A118831/A118832; variants: A118821, A118824, A118827; A100338.
Sequence in context: A006519 A055975 A118827 this_sequence A087258 A076775 A079891
Adjacent sequences: A118827 A118828 A118829 this_sequence A118831 A118832 A118833
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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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