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 A031511 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 13. 0
 171, 179, 187, 191, 199, 211, 223, 680, 704, 768, 800, 808, 832, 864, 872, 896, 1527, 1587, 1671, 1815, 1875, 1959, 2019, 2712, 2776, 2824, 3032, 3208, 3288, 3352, 3464, 3544, 3592, 4235, 4315, 4415, 4435, 4535, 4615, 4735, 4815, 4835, 4915, 5035, 5135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS MATHEMATICA ct13Q[n_]:=Module[{s=Sqrt[n], cf}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[ s][[2]]]; EvenQ[Length[cf]]&&cf[[(Length[cf])/2]] == 13]; Select[Range[5200], ct13Q] (* Harvey P. Dale, Sep 04 2018 *) CROSSREFS Sequence in context: A187140 A185845 A045149 * A101273 A136365 A031900 Adjacent sequences:  A031508 A031509 A031510 * A031512 A031513 A031514 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)