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Period of continued fraction for sqrt(n) contains no 1's.
3

%I #8 Jun 06 2021 18:17:19

%S 2,5,6,10,11,12,17,18,20,26,27,28,30,37,38,39,40,41,42,50,51,55,56,65,

%T 66,68,72,82,83,84,87,89,90,101,102,104,105,110,122,123,126,128,130,

%U 131,132,145,146,147,148,150,152,155,156,170,171,174,177,180,182,197,198,200,203

%N Period of continued fraction for sqrt(n) contains no 1's.

%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="/A013647/b013647.txt">Table of n, a(n) for n = 1..1000</a>

%t cf1Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],False,FreeQ[ ContinuedFraction[ s][[2]],1]]]; Select[Range[250],cf1Q] (* _Harvey P. Dale_, Jun 06 2021 *)

%K nonn

%O 1,1

%A _Clark Kimberling_