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 A002668 M1900 N0748 #32 Feb 16 2025 08:32:26
%S A002668 2,8,75,8949,119646723,15849841722437093,
%T A002668 708657580163382065836292133774995,
%U A002668 529026553215766321676623343348414600292754204772300344704877695232
%N A002668 Continued cotangent for e.
%D A002668 D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
%D A002668 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002668 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002668 Harry J. Smith, <a href="/A002668/b002668.txt">Table of n, a(n) for n = 1..11</a>
%H A002668 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 A002668 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>
%t A002668 b[1] = E; b[n_] := b[n] = (b[n-1]*Floor[b[n-1]]+1) / (b[n-1]-Floor[b[n-1]]); a[n_] := Floor[b[n]]; Table[a[n], {n, 1, 8}] (* _Jean-François Alcover_, Jan 17 2012, after PARI *)
%o A002668 (PARI) { default(realprecision, 10000); bn=vector(11); bn[1]=exp(1); for(n=2, 11, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 11, write("b002668.txt", n, " ", floor(bn[n]))); } \\ _Harry J. Smith_, May 04 2009
%K A002668 nonn,easy,nice
%O A002668 1,1
%A A002668 _N. J. A. Sloane_
%E A002668 More terms from _Jeffrey Shallit_