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A002666 Continued cotangent for square root of 2.
(Formerly M3983 N1652)
19

%I M3983 N1652

%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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Last modified May 19 10:55 EDT 2019. Contains 323390 sequences. (Running on oeis4.)