A031543 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 45.

2027, 2039, 2047, 2063, 2083, 2087, 2091, 2099, 2111, 2123, 2131, 2143, 2147, 2179, 2187, 2191, 2203, 2207, 8104, 8168, 8192, 8200, 8256, 8296, 8320, 8352, 8384, 8448, 8480, 8488, 8512, 8544, 8552, 8576, 8584, 8608, 8704, 8736, 8744, 8800, 8832, 18231

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Mathematica

cf45Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]]==45]; Select[Range[20000], cf45Q] (* Harvey P. Dale, Dec 04 2022 *)

Crossrefs

Sequence in context: A350869 A031768 A156856 * A031723 A145721 A103126

Adjacent sequences: A031540 A031541 A031542 * A031544 A031545 A031546

Keyword

nonn

Author

David W. Wilson

Status

approved