A031532 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 34.

1158, 1174, 1186, 1198, 1202, 1206, 1214, 1234, 1238, 1246, 1254, 1262, 1266, 1282, 1286, 1294, 2604, 2613, 2631, 2649, 2661, 2667, 2676, 2721, 2733, 2757, 2769, 2793, 2841, 2847, 2883, 2886, 2901, 2913, 4628, 4652, 4660, 4668, 4684, 4700, 4716, 4724

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

cf34Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[(len)/2]] == 34]; Select[Range[5000], cf34Q] (* Harvey P. Dale, Nov 29 2019 *)

Crossrefs

Sequence in context: A204478 A031746 A219148 * A168248 A237205 A358868

Adjacent sequences: A031529 A031530 A031531 * A031533 A031534 A031535

Keyword

nonn

Author

David W. Wilson

Status

approved