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A081790 Continued cotangent for tan(1). 0

%I

%S 1,4,32,1158,1815746,15716561494212,1184500978807872650350593387,

%T 5321879016477546178356935033926215638755808624425727229,

%U 28586857373644233013728565794450100157386617152409721820238727067747604580786570816033645416762395120483912199

%N Continued cotangent for tan(1).

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

%F tan(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tan(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]=tan(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 0,2

%A _Benoit Cloitre_, Apr 10 2003

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Last modified December 1 11:36 EST 2021. Contains 349429 sequences. (Running on oeis4.)