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 A002666 M3983 N1652 #36 Apr 25 2025 03:15:53
%S A002666 1,5,36,3406,14694817,727050997716715,2074744506784679417243551677046,
%T A002666 46045625970633183674340934067371917846908361831894602280765110
%N A002666 Continued cotangent for square root of 2.
%D A002666 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002666 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002666 Harry J. Smith, <a href="/A002666/b002666.txt">Table of n, a(n) for n = 0..11</a>
%H A002666 D. H. Lehmer, <a href="/A002065/a002065_1.pdf">A cotangent analogue of continued fractions</a>, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]
%H A002666 D. H. Lehmer, <a href="http://dx.doi.org/10.1215/S0012-7094-38-00424-7">A cotangent analogue of continued fractions</a>, Duke Math. J., 4 (1935), 323-340.
%H A002666 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>.
%t A002666 Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, Sqrt[2], 7]] (* _Stefano Spezia_, Apr 24 2025 *)
%o A002666 (PARI) { default(realprecision, 10000); bn=vector(12); bn[1]=sqrt(2); for(n=2, 12, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 12, print1(floor(bn[n]), ", ")); } \\ _Harry J. Smith_, May 04 2009
%K A002666 nonn
%O A002666 0,2
%A A002666 _N. J. A. Sloane_
%E A002666 More terms from _Jeffrey Shallit_