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Search: id:A118828
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| A118828 |
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Numerators of the convergents of the 2-adic continued fraction of zero given by A118827. |
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+0
4
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| 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, -1
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Period 8 sequence: [1,-1,0,-1,-1,1,0,1]. G.f.: (1-x-x^3)/(1+x^4).
a(n)=1/8*{-[(n+1) mod 8]+[(n+2) mod 8]-2*[(n+3) mod 8]+[(n+5) mod 8]-[(n+6) mod 8]+2*[(n+7) mod 8]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 27 2006
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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/(-1)^n.
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, v=vector(n, i, if(i%2==1, p, q*2^valuation(i/2, 2)))); contfracpnqn(v)[1, 1]}
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CROSSREFS
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Cf. A118827 (partial quotients), A118829 (denominators).
Sequence in context: A085369 A046980 A118831 this_sequence A071034 A105234 A005713
Adjacent sequences: A118825 A118826 A118827 this_sequence A118829 A118830 A118831
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KEYWORD
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frac,sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2006
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