This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081782 #24 Apr 25 2025 08:45:53
%S A081782 0,1,3,16,389,479403,590817544217,473341703003810973963339,
%T A081782 269963674630454468003021997747122421847127276823,
%U A081782 84255020180725066155718508782582560544360994462142096519461567461295107080386955008872752275165
%N A081782 Continued cotangent for the Gamma constant.
%H A081782 Stefano Spezia, <a href="/A081782/b081782.txt">Table of n, a(n) for n = 0..12</a>
%H A081782 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>
%F A081782 Gamma = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081782 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)).
%t A081782 Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, EulerGamma, 9]] (* _Stefano Spezia_, Apr 24 2025 *)
%o A081782 (PARI) bn=vector(100);
%o A081782 b(n)=if(n<0,0,bn[n]);
%o A081782 bn[1]=Euler;
%o A081782 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))))
%o A081782 a(n)=floor(b(n+1))
%Y A081782 Cf. A001620, A002666, A002667.
%K A081782 nonn
%O A081782 0,3
%A A081782 _Benoit Cloitre_, Apr 10 2003