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Search: id:A081787
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| A081787 |
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Continued cotangent for sqrt(e). |
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+0
1
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| 1, 4, 208, 51198, 3265038057, 25300257957809599598, 1548008157389016603196793951803038609594, 15445738611564165990406534887324277271178568836676520360367688416251534382546319
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
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FORMULA
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sqrt(e)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(e), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n))
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PROGRAM
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(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=sqrt(e); ?for(n=2, 10, bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1))
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CROSSREFS
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Cf. A002666, A002667, A002668.
Sequence in context: A049656 A129465 A087924 this_sequence A038790 A042325 A091287
Adjacent sequences: A081784 A081785 A081786 this_sequence A081788 A081789 A081790
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 10 2003
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