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A081789 Continued cotangent for cos(1). 0

%I

%S 0,1,3,31,1896,4466398,51545652359935,7892797673015743066290382811,

%T 79208317703482281896053478218775642522933780224074809198,

%U 195824124605155340760338534459689354174423866004140103635128465652592661899008938733448659610261796713081609084855

%N Continued cotangent for cos(1).

%D D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

%F cos(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=cos(1), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n)).

%o (PARI) ?bn=vector(100); b(n)=if(n<0,0,bn[n]); bn[1]=cos(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))

%Y Cf. A002666, A002667, A002668.

%K nonn

%O 0,3

%A _Benoit Cloitre_, Apr 10 2003

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Last modified January 18 11:29 EST 2022. Contains 350454 sequences. (Running on oeis4.)