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Search: id:A081791
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| A081791 |
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Continued cotangent for sinh(1). |
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+0
1
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| 1, 12, 361, 6098638, 40523300374005, 2249947521757014011818803347, 23934989997298328927868650983263126279480229971908985849, 2858972935444266747494645602151444724302966656792002957565134720098726922500919331865545624811189334200411357440
(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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sinh(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sinh(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]=sinh(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.
Adjacent sequences: A081788 A081789 A081790 this_sequence A081792 A081793 A081794
Sequence in context: A012385 A012430 A012632 this_sequence A024298 A081021 A138914
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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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