|
|
A081792
|
|
Continued cotangent for cosh(1).
|
|
0
|
|
|
1, 4, 28, 898, 865865, 6558406221253, 369641727028862496144018420, 168218383805281752399017936550348552720479497871513674, 46139813370820669084709611625366168409170012365100187639338625228748249752136723842763775088752136299316085
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
|
|
LINKS
|
|
|
FORMULA
|
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))
|
|
PROG
|
(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))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|