A031408 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 5.

27, 31, 43, 47, 104, 128, 160, 192, 231, 303, 375, 408, 435, 472, 536, 635, 664, 715, 776, 815, 835, 912, 1115, 1135, 1215, 1239, 1267, 1464, 1488, 1575, 1603, 1616, 1631, 1712, 1744, 1752, 1840, 1883, 1967, 1968, 2000, 2043, 2051, 2096, 2135, 2224, 2259

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]] == 5, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
ep5Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 5]; Select[ Range[ 2500], ep5Q] (* Harvey P. Dale, Apr 24 2016 *)

Crossrefs

Cf. A031404-A031423.

Sequence in context: A316729 A095387 A228060 * A324248 A275188 A198147

Adjacent sequences: A031405 A031406 A031407 * A031409 A031410 A031411

Keyword

nonn

Author

David W. Wilson

Status

approved