A013647 Numbers k such that the period of the continued fraction for sqrt(k) contains no 1'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, 66, 68, 72, 82, 83, 84, 87, 89, 90, 101, 102, 104, 105, 110, 122, 123, 126, 128, 130, 131, 132, 145, 146, 147, 148, 150, 152, 155, 156, 170, 171, 174, 177, 180, 182, 197, 198, 200, 203

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Programs

Mathematica

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 *)