A081794 - OEIS

%I #9 Mar 30 2012 18:39:16

%S 0,1,8,211,114681,118304381067,14093169772574392414247,

%T 233069007722838136376547872705625127588988391,

%U 148096265277934997326846757550268707006396575812305676278686643630022889932579135326452726

%N Continued cotangent for Pi/4.

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

%F Pi/4=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi/4, 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/4; ?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