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A013642 Numbers n such that continued fraction for sqrt(n) has period 2. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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: A308221 A277732 A026604 * A140482 A212451 A244223

Adjacent sequences:  A013639 A013640 A013641 * A013643 A013644 A013645

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)