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Search: id:A081783
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| A081783 |
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Continued cotangent for zeta(2)=Pi^2/6. |
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+0
1
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| 1, 4, 172, 181307, 241328833528, 824652019956267685427678, 768422457901766762303892554138930904416139509281, 21106880566309019070608778967379323765079362642683820764565392361458497091484810\ 95915090382331184
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OFFSET
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0,2
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FORMULA
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Pi^2/6=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi^2/6, 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]=Pi^2/6; ?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. A001620, A002666, A002667.
Sequence in context: A051476 A057140 A145245 this_sequence A006433 A113254 A127606
Adjacent sequences: A081780 A081781 A081782 this_sequence A081784 A081785 A081786
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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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