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A013642 Numbers n such that continued fraction for sqrt(n) has period 2. 7


%S 3,6,8,11,12,15,18,20,24,27,30,35,38,39,40,42,48,51,56,63,66,68,72,80,

%T 83,84,87,90,99,102,104,105,110,120,123,132,143,146,147,148,150,152,

%U 156,168,171,182,195,198,200,203,210,224,227,228,230,231,235,240,255,258,260,264

%N Numbers n such that continued fraction for sqrt(n) has period 2.

%C This sequence is identical to the sequence of numbers of the form n = a^2 + b, where a and b are positive integers and b is a factor of 2a greater than 1, in which case the continued fraction expansion of sqrt(n) is [a; [2a/b, 2a]]. - _David Terr_, Jun 11 2004

%D Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!)

%H T. D. Noe, <a href="/A013642/b013642.txt">Table of n, a(n) for n = 1..1000</a>

%t cf2Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],1,Length[ ContinuedFraction[ s][[2]]]]==2]; Select[Range[300],cf2Q] (* _Harvey P. Dale_, Jun 21 2017 *)

%Y Cf. A001066, A043549, A026604, A047219, A090848, A004957.

%K nonn

%O 1,1

%A _Clark Kimberling_

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Last modified January 28 03:28 EST 2020. Contains 331314 sequences. (Running on oeis4.)