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A081793
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Continued cotangent for tanh(1).
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0
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0, 1, 7, 135, 35445, 44465908998, 5112887721516309845621, 75234509360529020708450352828794956245887456, 5786575206590910267083400178061771765781639734324927167565054640197289842752623499343753
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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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LINKS
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Table of n, a(n) for n=0..8.
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FORMULA
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tanh(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tanh(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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PROG
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(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=tanh(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: A143181 A183478 A292395 * A296595 A210028 A243684
Adjacent sequences: A081790 A081791 A081792 * A081794 A081795 A081796
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Apr 10 2003
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STATUS
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approved
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