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%I M3034 N1230 #23 Dec 20 2021 20:11:43
%S 1,1,3,16,547,538811,620245817465,692770666469127829226736,
%T 1025344764595988314871439243086711931108916434521
%N Numerators of convergents to Lehmer's constant.
%D D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
%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).
%D J. W. Wrench, Jr., personal communication.
%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 J. W. Wrench, Jr., <a href="/A002065/a002065_2.pdf">Letters to N. J. A. Sloane, Feb 1974</a>
%t Block[{$MaxExtraPrecision=1000},Numerator[Convergents[With[{nn=15},Cot[ Total[Last[#] ArcCot[First[#]]&/@Thread[{NestList[#^2+#+1&,0,nn], PadRight[{},nn+1,{1,-1}]}]]]],10]]] (* _Harvey P. Dale_, Jan 29 2012 *)
%Y Cf. A002794, A002795, A002665, A030125, A002065.
%K nonn,frac,nice
%O 0,3
%A _N. J. A. Sloane_
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