A031620 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 32.

13274, 21106, 21397, 21985, 44269, 58789, 75914, 77573, 78689, 93997, 96461, 114685, 116041, 118777, 120157, 139658, 143413, 162229, 163034, 163841, 167906, 169546, 170369, 196093, 219865, 227417, 229325, 249962, 250961, 252965, 253970

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

cf32Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,1},ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len]&&cf[[Floor[len/2]]]==cf[[Ceiling[len/2]]] == 32]; Select[ Range[254000],cf32Q] (* Harvey P. Dale, May 01 2022 *)

Extensions

First term 1025 removed by Georg Fischer, Jun 16 2019