login
A081795
Continued cotangent for Pi/3.
0
1, 43, 4975, 87377992, 18385473430682423, 5186411232443302687031694765612941, 47469894147223278266560159220413635233953187522490823346090207081760
OFFSET
0,2
REFERENCES
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 10 2003
STATUS
approved