A081782 Continued cotangent for the Gamma constant.

0, 1, 3, 16, 389, 479403, 590817544217, 473341703003810973963339, 269963674630454468003021997747122421847127276823, 84255020180725066155718508782582560544360994462142096519461567461295107080386955008872752275165

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Links

• Stefano Spezia, Table of n, a(n) for n = 0..12
• Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion

Crossrefs

Cf. A001620, A002666, A002667.

Programs

Mathematica

Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, EulerGamma, 9]] (* Stefano Spezia, Apr 24 2025 *)

PARI

bn=vector(100);
b(n)=if(n<0,0,bn[n]);
bn[1]=Euler;
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))

Formula

Gamma = cot(Sum_{n>=0} (-1)^n*acot(a(n))).

Let b(0) = Gamma, b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).