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Search: id:A118825
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| A118825 |
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Numerators of the convergents of the 2-adic continued fraction of zero given by A118824. |
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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
(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*{3*[n mod 8]-[(n+1) mod 8]+(n+2) mod 8+(n+3) mod 8-3*[(n+4) mod 8]+(n+5) mod 8-[(n+6) mod 8]-[(n+7) mod 8] - Paolo P. Lava (ppl(AT)spl.at), Oct 20 2006
a(n)=1/8*{3*(n mod 8)-[(n+1) mod 8]+[(n+2) mod 8]+[(n+3) mod 8]-3*[(n+4) mod 8]+[(n+5) mod 8]-[(n+6) mod 8]-[(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 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/(-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. A118824 (partial quotients), A118826 (denominators).
Sequence in context: A096661 A098178 A007877 this_sequence A118822 A054848 A065368
Adjacent sequences: A118822 A118823 A118824 this_sequence A118826 A118827 A118828
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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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