A031515 Numbers k such 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 17.

291, 307, 311, 331, 339, 343, 347, 359, 1160, 1184, 1192, 1216, 1248, 1256, 1280, 1312, 1344, 1352, 1376, 1384, 1408, 1440, 2607, 2823, 2895, 2955, 3039, 3183, 3243, 4632, 4696, 4744, 4824, 4952, 5016, 5128, 5144, 5272, 5384, 5464, 5528, 5592, 5768, 7235

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Mathematica

okQ[k_] := Module[{c, lc}, If[IntegerQ[Sqrt[k]], False,
     c = ContinuedFraction[Sqrt[k]]; lc = Length[c[[2]]];
     EvenQ[lc] && c[[2, lc/2]] == 17]];
Select[Range[10000], okQ] (* Jean-François Alcover, Jul 09 2021 *)

Crossrefs

Sequence in context: A186548 A091740 A098250 * A352536 A090890 A123913

Adjacent sequences: A031512 A031513 A031514 * A031516 A031517 A031518

Keyword

nonn

Author

David W. Wilson

Status

approved