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A081795 Continued cotangent for Pi/3. 0


%S 1,43,4975,87377992,18385473430682423,

%T 5186411232443302687031694765612941,

%U 47469894147223278266560159220413635233953187522490823346090207081760

%N Continued cotangent for Pi/3.

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

%F Pi/3=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi/3, 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]=Pi/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))

%Y Cf. A002666, A002667, A002668.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Apr 10 2003

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)