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A013642
Numbers k such that the continued fraction for sqrt(k) has period 2.
9
3, 6, 8, 11, 12, 15, 18, 20, 24, 27, 30, 35, 38, 39, 40, 42, 48, 51, 56, 63, 66, 68, 72, 80, 83, 84, 87, 90, 99, 102, 104, 105, 110, 120, 123, 132, 143, 146, 147, 148, 150, 152, 156, 168, 171, 182, 195, 198, 200, 203, 210, 224, 227, 228, 230, 231, 235, 240, 255, 258, 260, 264
OFFSET
1,1
COMMENTS
This sequence is identical to the sequence of numbers of the form k = 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(k) is [a; [2a/b, 2a]]. - David Terr, Jun 11 2004
REFERENCES
Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!)
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
STATUS
approved