A081792 - OEIS

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

%S 1,4,28,898,865865,6558406221253,369641727028862496144018420,

%T 168218383805281752399017936550348552720479497871513674,

%U 46139813370820669084709611625366168409170012365100187639338625228748249752136723842763775088752136299316085

%N Continued cotangent for cosh(1).

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

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