A081781 Continued cotangent for square root of 5.

2, 23, 2961, 9798690, 110528843365255, 16850689692769666225948933906, 357017084742873887104901208145335336566095925224005385073, 137046393407742688281781643318644289249627231296779665713406441509975367310318242383523303176564909084594247359836

Offset

0,1

Links

Table of n, a(n) for n=0..7.

Formula

sqrt(5)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(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]=sqrt(5); ?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.

Sequence in context: A227529 A091763 A124513 * A088734 A087388 A117507

Adjacent sequences: A081778 A081779 A081780 * A081782 A081783 A081784

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved