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A020396 Numbers k such that the continued fraction for sqrt(k) has period 57. 1

%I #26 Jul 11 2021 12:19:59

%S 1453,1609,2593,4297,4474,4937,5914,6385,6442,7066,7309,7853,8425,

%T 8593,8741,9137,9193,10057,10133,10973,11117,11554,12641,13613,13957,

%U 14185,14585,14633,15137,15866,17285,17354,18077,18241,18413,19666,20290,20794

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

%C Smallest term that is not squarefree is 8425, as sqrt(8425) = 5 * sqrt(337). - _Alonso del Arte_, Mar 10 2018

%H Vincenzo Librandi, <a href="/A020396/b020396.txt">Table of n, a(n) for n = 1..300</a>

%t 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 *)

%t Select[Range[30000], Length[Last[ContinuedFraction[Sqrt[#]]]] == 57 &] (* _Vincenzo Librandi_, Mar 11 2018, after _Alonso del Arte_ *)

%K nonn

%O 1,1

%A _David W. Wilson_

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Last modified July 23 03:47 EDT 2024. Contains 374544 sequences. (Running on oeis4.)