A031514 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 16.

258, 262, 278, 302, 322, 579, 597, 633, 651, 654, 669, 681, 687, 717, 726, 1028, 1052, 1060, 1068, 1076, 1084, 1108, 1116, 1124, 1132, 1148, 1164, 1172, 1212, 1228, 1244, 1252, 1268, 1276, 1292, 1605, 1630, 1645, 1655, 1670, 1795, 1805, 1830, 1895, 1905

Offset

1,1

Links

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

Mathematica

cf16Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len] && cf[[len/2]] == 16]; Select[Range[2000], cf16Q] (* Harvey P. Dale, Mar 04 2018 *)

Crossrefs

Sequence in context: A121237 A161683 A250741 * A173981 A339538 A252264

Adjacent sequences: A031511 A031512 A031513 * A031515 A031516 A031517

Keyword

nonn

Author

David W. Wilson

Status

approved