Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 3.
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Subsequence of A003814.
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Numbers n k such that the continued fraction for sqrt(nk) has odd period and a pair of central terms both equal to 3.
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cfo3Q[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]] == cf[[(len-1)/2]]==3]; Select[Range[3300], cfo3Q] (* Harvey P. Dale, Sep 25 2019 *)
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Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central term terms both equal to 3.
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