A031410 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 7.

51, 59, 67, 71, 79, 200, 232, 296, 320, 447, 519, 591, 723, 792, 856, 984, 1048, 1112, 1235, 1288, 1315, 1335, 1415, 1435, 1535, 1715, 1735, 1776, 1835, 1915, 2015, 2064, 2415, 2443, 2527, 2616, 2779, 2904, 3152, 3227, 3376, 3504, 3535, 3563, 3619, 3632

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]] == 7, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
cf7Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len = Length[cf]; EvenQ[len]&&cf[[len/2]] == 7]; Select[Range[3700], cf7Q] (* Harvey P. Dale, Aug 23 2021 *)

Crossrefs

Cf. A031404-A031423.

Sequence in context: A095525 A045805 A373205 * A308766 A039387 A043210

Adjacent sequences: A031407 A031408 A031409 * A031411 A031412 A031413

Keyword

nonn

Author

David W. Wilson

Status

approved