A010337 Numbers k such that the continued fraction for sqrt(k) has period 5.

13, 29, 53, 74, 85, 89, 125, 173, 185, 218, 229, 293, 338, 346, 365, 373, 445, 533, 557, 629, 701, 733, 818, 845, 914, 925, 965, 985, 1009, 1042, 1093, 1105, 1129, 1145, 1229, 1373, 1378, 1490, 1525, 1685, 1853, 1901, 1970, 2029, 2138, 2213, 2362, 2378, 2405

Offset

1,1

Links

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

Peter H. van der Kamp, Anthony Overmars, Marcel Jackson, and Andrew Hone, On efficient approximation of quadratic irrationals, arXiv:2511.21617 [math.NT], 2025. See references.

Mathematica

q[k_] := Module[{c = ContinuedFraction[Sqrt[k]]}, Length[c] == 2 && Length[c[[2]]] == 5]; Select[Range[2500], q] (* Amiram Eldar, Aug 21 2025 *)

Crossrefs

Sequence in context: A370238 A031414 A270361 * A244637 A162579 A286658

Adjacent sequences: A010334 A010335 A010336 * A010338 A010339 A010340

Keyword

nonn

Author

N. J. A. Sloane and Walter Gilbert

Status

approved