A081790 Continued cotangent for tan(1).

1, 4, 32, 1158, 1815746, 15716561494212, 1184500978807872650350593387, 5321879016477546178356935033926215638755808624425727229, 28586857373644233013728565794450100157386617152409721820238727067747604580786570816033645416762395120483912199

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..8.

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))

Prog

(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: A298896 A231991 A028369 * A053005 A257583 A258122

Adjacent sequences: A081787 A081788 A081789 * A081791 A081792 A081793

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved