A081780 Continued cotangent for square root of 3.

1, 3, 16, 405, 672320, 1352290629546, 4817801789405093582066881, 125242334906904794515426191021121381708761081802849, 48098205042808280233282792304806428848378744166690329294696649253234314988369597043479633480454760546

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

sqrt(3)=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(3); ?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: A054939 A081782 A176299 * A362382 A297118 A002794

Adjacent sequences: A081777 A081778 A081779 * A081781 A081782 A081783

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved