A013642 Numbers k such that the continued fraction for sqrt(k) has period 2.

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!)

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

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

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

Sequence in context: A350546 A277732 A026604 * A140482 A212451 A244223

Adjacent sequences: A013639 A013640 A013641 * A013643 A013644 A013645

Keyword

nonn

Author

Clark Kimberling

Status

approved