A020396 Numbers k such that the continued fraction for sqrt(k) has period 57.

1453, 1609, 2593, 4297, 4474, 4937, 5914, 6385, 6442, 7066, 7309, 7853, 8425, 8593, 8741, 9137, 9193, 10057, 10133, 10973, 11117, 11554, 12641, 13613, 13957, 14185, 14585, 14633, 15137, 15866, 17285, 17354, 18077, 18241, 18413, 19666, 20290, 20794

Offset

1,1

Comments

Smallest term that is not squarefree is 8425, as sqrt(8425) = 5 * sqrt(337). - Alonso del Arte, Mar 10 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Mathematica

cf57Q[n_] := Module[{s = Sqrt[n]}, If[IntegerQ[s], 1, Length[ContinuedFraction[s][[2]]]] == 57]; Select[Range[21000], cf57Q] (* Harvey P. Dale, Feb 12 2015 *)
Select[Range[30000], Length[Last[ContinuedFraction[Sqrt[#]]]] == 57 &] (* Vincenzo Librandi, Mar 11 2018, after Alonso del Arte *)

Crossrefs

Sequence in context: A151722 A250148 A068280 * A052237 A031613 A289822

Adjacent sequences: A020393 A020394 A020395 * A020397 A020398 A020399

Keyword

nonn

Author

David W. Wilson

Status

approved