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Search: id:A081789
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| A081789 |
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Continued cotangent for cos(1). |
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+0
1
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| 0, 1, 3, 31, 1896, 4466398, 51545652359935, 7892797673015743066290382811, 79208317703482281896053478218775642522933780224074809198, 195824124605155340760338534459689354174423866004140103635128465652592661899008938733448659610261796713081609084855
(list; graph; listen)
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OFFSET
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0,3
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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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cos(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=cos(1), 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]=cos(1); ?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: A094579 A029729 A136584 this_sequence A066976 A048562 A022499
Adjacent sequences: A081786 A081787 A081788 this_sequence A081790 A081791 A081792
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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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