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A081796
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Continued cotangent for sin(Pi/3)=sqrt(3)/2.
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0
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0, 1, 13, 196, 257087, 249639161983, 553029809670900697241813, 575598315149214535162520163688459972096324096213, 680813056961507163626080261194823226597566577785481001106845521689287461487322891517719568410606
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OFFSET
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0,3
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 433-434.
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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FORMULA
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sqrt(3)/2=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(3)/2, 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]=sqrt(3)/2; ?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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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