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Search: id:A118831
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| A118831 |
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Numerators of the convergents of the 2-adic continued fraction of zero given by A118830. |
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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
(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*{2*(n mod 8)-[(n+1) mod 8]+[(n+2) mod 8]-2*[(n+4) mod 8]+[(n+5) mod 8]-[(n+6) 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 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, 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. A118830 (partial quotients), A118832 (denominators).
Sequence in context: A004547 A085369 A046980 this_sequence A118828 A071034 A105234
Adjacent sequences: A118828 A118829 A118830 this_sequence A118832 A118833 A118834
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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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