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Search: id:A118822
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| A118822 |
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Numerators of the convergents of the 2-adic continued fraction of zero given by A118821. |
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+0
3
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| 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -1, 0, -1, -2, 1, 0, 1, 2, -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: [2,-1,0,-1,-2,1,0,1]. G.f.: (2-x-x^3)/(1+x^4).
a(n)=-1/8*{n mod 8+(n+1) mod 8-[(n+2) mod 8]+3*[(n+3) mod 8]-[(n+4) mod 8]-[(n+5) mod 8]+(n+6) mod 8-3*[(n+7) mod 8]} - Paolo P. Lava (ppl(AT)spl.at), Oct 20 2006
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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, 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. A118821 (partial quotients), A118823 (denominators).
Sequence in context: A098178 A007877 A118825 this_sequence A054848 A065368 A010751
Adjacent sequences: A118819 A118820 A118821 this_sequence A118823 A118824 A118825
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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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