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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

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

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

Cf. A002666, A002667, A002668.

Sequence in context: A101346 A120604 A203279 * A336622 A084594 A334598

Adjacent sequences:  A081789 A081790 A081791 * A081793 A081794 A081795

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

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Last modified November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)