A081792 Continued cotangent for cosh(1).

1, 4, 28, 898, 865865, 6558406221253, 369641727028862496144018420, 168218383805281752399017936550348552720479497871513674, 46139813370820669084709611625366168409170012365100187639338625228748249752136723842763775088752136299316085

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..8.

Formula

cosh(1) = cot(Sum_{n>=0} (-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)).

Prog

(PARI) \p900
bn=vector(100);
bn[1]=cosh(1);
b(n)=if(n<0, 0, bn[n]);
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));

Crossrefs

Cf. A002666, A002667, A002668.

Sequence in context: A101346 A120604 A203279 * A336622 A354842 A084594

Adjacent sequences: A081789 A081790 A081791 * A081793 A081794 A081795

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved