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A020396 Numbers k such that the continued fraction for sqrt(k) has period 57. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 14:12 EST 2022. Contains 350455 sequences. (Running on oeis4.)