A020395 Numbers k such that the continued fraction for sqrt(k) has period 56.

1039, 1852, 1948, 2188, 2497, 2529, 3022, 3343, 3799, 3884, 3911, 3937, 4079, 4124, 4390, 4405, 4423, 4540, 4679, 4943, 5433, 5646, 5764, 6141, 6244, 6332, 6334, 6428, 6505, 7017, 7255, 7495, 7525, 7708, 7792, 7806, 7813, 7821, 7852, 7882, 7916, 8071

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

q[k_] := Module[{c = ContinuedFraction[Sqrt[k]]}, Length[c] == 2 && Length[c[[2]]] == 56]; Select[Range[9000], q] (* Amiram Eldar, Aug 23 2025 *)
cf56Q[n_]:=With[{s=Sqrt[n]}, If[IntegerQ[s], 1, Length[ContinuedFraction[s][[2]]]]==56]; Select[Range[8100], cf56Q] (* Harvey P. Dale, Dec 21 2025 *)

Crossrefs

Cf. A003285.

Sequence in context: A074673 A235156 A288413 * A069456 A210259 A233854

Adjacent sequences: A020392 A020393 A020394 * A020396 A020397 A020398

Keyword

nonn

Author

David W. Wilson

Status

approved