|
Search: id:A081793
|
|
|
| A081793 |
|
Continued cotangent for tanh(1). |
|
+0
1
|
|
| 0, 1, 7, 135, 35445, 44465908998, 5112887721516309845621, 75234509360529020708450352828794956245887456, 5786575206590910267083400178061771765781639734324927167565054640197289842752623499343753
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
|
|
FORMULA
|
tanh(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tanh(1), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n))
|
|
PROGRAM
|
(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=tanh(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.
Adjacent sequences: A081790 A081791 A081792 this_sequence A081794 A081795 A081796
Sequence in context: A003374 A001533 A143181 this_sequence A051504 A058881 A100520
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 10 2003
|
|
|
Search completed in 0.002 seconds
|
