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%I M3983 N1652 #29 Oct 18 2023 04:31:53
%S 1,5,36,3406,14694817,727050997716715,2074744506784679417243551677046,
%T 46045625970633183674340934067371917846908361831894602280765110
%N Continued cotangent for square root of 2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Harry J. Smith, <a href="/A002666/b002666.txt">Table of n, a(n) for n = 0..11</a>
%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>.
%o (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, write("b002666.txt", n-1, " ", floor(bn[n]))); } \\ _Harry J. Smith_, May 04 2009
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Jeffrey Shallit_
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