A031404 Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 1.

3, 7, 8, 15, 24, 32, 35, 48, 63, 75, 80, 88, 91, 99, 115, 120, 135, 136, 143, 168, 175, 176, 195, 208, 215, 224, 247, 255, 279, 280, 288, 304, 312, 319, 323, 360, 399, 403, 427, 432, 440, 464, 483, 528, 539, 551, 555, 560, 575, 595, 611, 624, 671, 675, 696

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A031405-A031423.

Programs

Mathematica

n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && c[[2, len/2]] == 1, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)

Extensions

Names of A031404-A031423 clarified by N. J. A. Sloane, Aug 18 2021