A081796 Continued cotangent for sin(Pi/3) = sqrt(3)/2.

0, 1, 13, 196, 257087, 249639161983, 553029809670900697241813, 575598315149214535162520163688459972096324096213, 680813056961507163626080261194823226597566577785481001106845521689287461487322891517719568410606

Offset

0,3

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 433-434.

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.

Steven R. Finch, Lehmer's Constant [broken link]

Steven R. Finch, Lehmer's Constant [From the Wayback machine]

Formula

sqrt(3)/2 = cot(Sum_{n>=0} (-1)^n*acot(a(n))).

Let b(0) = sqrt(3)/2, 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) \p900
bn=vector(100);
bn[1]=sqrt(3)/2;
b(n)=if(n<0, 0, bn[n]);
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. A002065, A002666, A002667, A002668.

Sequence in context: A015690 A027773 A099271 * A140536 A289734 A130549

Adjacent sequences: A081793 A081794 A081795 * A081797 A081798 A081799

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved