|
Search: id:A081790
|
|
|
| A081790 |
|
Continued cotangent for tan(1). |
|
+0
1
|
|
| 1, 4, 32, 1158, 1815746, 15716561494212, 1184500978807872650350593387, 5321879016477546178356935033926215638755808624425727229, 28586857373644233013728565794450100157386617152409721820238727067747604580786570816033645416762395120483912199
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
|
|
FORMULA
|
tan(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tan(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]=tan(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: A132854 A136471 A028369 this_sequence A053005 A012092 A027639
Adjacent sequences: A081787 A081788 A081789 this_sequence A081791 A081792 A081793
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 10 2003
|
|
|
Search completed in 0.002 seconds
|
