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Search: id:A118824
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| A118824 |
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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, -2, 1, -2, 2, -2, 1
(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: A118821, 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 A118825(k)/A118826(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.
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: A118825/A118826; variants: A118821, A118827, A118830; A100338.
Sequence in context: A099910 A043555 A118821 this_sequence A082641 A138553 A069016
Adjacent sequences: A118821 A118822 A118823 this_sequence A118825 A118826 A118827
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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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