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

Author

N. J. A. Sloane and Walter Gilbert

Keywords

• nonn
• changed

Links

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

Programs

Mathematica

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