A031516 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 18.

326, 334, 354, 358, 374, 382, 386, 398, 732, 741, 753, 789, 804, 813, 831, 849, 897, 1300, 1324, 1340, 1348, 1356, 1372, 1388, 1396, 1412, 1436, 1452, 1460, 1468, 1492, 1500, 1516, 1532, 1548, 1556, 1564, 1588, 1596, 2030, 2045, 2095, 2105, 2155, 2195

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Mathematica

cf18Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 18]; Select[Range[2200], cf18Q] (* Harvey P. Dale, May 26 2018 *)

Crossrefs

Sequence in context: A048918 A274307 A358148 * A066128 A138816 A138817

Adjacent sequences: A031513 A031514 A031515 * A031517 A031518 A031519

Keyword

nonn

Author

David W. Wilson

Status

approved