A031406 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 3.

11, 19, 23, 40, 87, 96, 152, 159, 216, 219, 235, 335, 336, 344, 392, 415, 455, 515, 535, 567, 592, 615, 688, 707, 747, 816, 848, 875, 888, 920, 927, 944, 976, 1072, 1080, 1099, 1111, 1143, 1183, 1199, 1200, 1211, 1243, 1320, 1328, 1359, 1360, 1456, 1507, 1547

Offset

1,1

Links

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

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]] == 3, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
cf3Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 3]; Select[Range[1600], cf3Q] (* Harvey P. Dale, Aug 15 2015 *)

Crossrefs

Cf. A031404-A031423.

Sequence in context: A359401 A161601 A352480 * A280993 A352925 A105908

Adjacent sequences: A031403 A031404 A031405 * A031407 A031408 A031409

Keyword

nonn

Author

David W. Wilson

Status

approved