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A081794 Continued cotangent for Pi/4. 0
0, 1, 8, 211, 114681, 118304381067, 14093169772574392414247, 233069007722838136376547872705625127588988391, 148096265277934997326846757550268707006396575812305676278686643630022889932579135326452726 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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))

PROG

(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))

CROSSREFS

Cf. A002666, A002667, A002668.

Sequence in context: A197980 A197767 A024288 * A221042 A247032 A027646

Adjacent sequences:  A081791 A081792 A081793 * A081795 A081796 A081797

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.)