|
Search: id:A081788
|
|
|
| A081788 |
|
Continued cotangent for sin(1). |
|
+0
1
|
|
| 0, 1, 11, 209, 778615, 3961986619787, 108027609649678328362291208, 12797763868538691769539594849146740548395979750179143, 23987058893231178482340639410750933044770048099962031968769042922030621378334112\ 76780250923333345577605421
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
|
|
FORMULA
|
sin(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sin(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]=sin(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: A020518 A131216 A034909 this_sequence A060496 A157691 A112386
Adjacent sequences: A081785 A081786 A081787 this_sequence A081789 A081790 A081791
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 10 2003
|
|
|
Search completed in 0.002 seconds
|
