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Search: id:A081790
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| A081790 |
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Continued cotangent for tan(1). |
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+0
1
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| 1, 4, 32, 1158, 1815746, 15716561494212, 1184500978807872650350593387, 5321879016477546178356935033926215638755808624425727229, 28586857373644233013728565794450100157386617152409721820238727067747604580786570\ 816033645416762395120483912199
(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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tan(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tan(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]=tan(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: A132854 A136471 A028369 this_sequence A053005 A012092 A027639
Adjacent sequences: A081787 A081788 A081789 this_sequence A081791 A081792 A081793
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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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