A031628 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 40.

401, 10429, 20498, 32842, 33937, 68813, 90826, 92641, 94474, 178525, 180217, 213973, 214898, 216754, 251626, 252629, 253634, 254641, 256661, 257674, 259706, 262769, 344237, 346585, 348941, 353677, 386602, 392837, 396602, 400385, 439333, 443314, 449989

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

op40Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{0,0}, ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len]&&cf[[(len+1)/2]] ==40]; Select[Range[500000],op40Q] (* Harvey P. Dale, Dec 06 2015 *)

Extensions

Corrected and extended by Harvey P. Dale, Dec 06 2015