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A081795 Continued cotangent for Pi/3. 0
1, 43, 4975, 87377992, 18385473430682423, 5186411232443302687031694765612941, 47469894147223278266560159220413635233953187522490823346090207081760 (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..6.

FORMULA

Pi/3=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi/3, 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/3; ?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: A145315 A110704 A060485 * A108837 A091748 A208625

Adjacent sequences:  A081792 A081793 A081794 * A081796 A081797 A081798

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

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Last modified October 16 06:14 EDT 2021. Contains 348040 sequences. (Running on oeis4.)