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Search: id:A081780
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| A081780 |
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Continued cotangent for square root of 3. |
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+0
1
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| 1, 3, 16, 405, 672320, 1352290629546, 4817801789405093582066881, 125242334906904794515426191021121381708761081802849, 48098205042808280233282792304806428848378744166690329294696649253234314988369597\ 043479633480454760546
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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sqrt(3)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(3), 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]=sqrt(3); ?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.
Sequence in context: A005031 A054939 A081782 this_sequence A002794 A132559 A080273
Adjacent sequences: A081777 A081778 A081779 this_sequence A081781 A081782 A081783
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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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