A031606 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 18.

82, 2141, 4274, 6970, 7306, 10525, 10937, 14569, 15053, 18994, 20389, 24314, 25253, 25889, 30637, 31337, 36541, 43793, 47618, 51701, 52154, 52609, 53066, 54449, 55381, 62233, 70537, 71597, 72665, 80485, 81050, 82757, 83905, 85061, 85642, 86225, 86810

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

opct18Q[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]] == 18]; Select[Range[90000],opct18Q] (* Harvey P. Dale, Nov 12 2013 *)

Extensions

Corrected by Harvey P. Dale, Nov 12 2013