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A031416
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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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1
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89, 149, 193, 218, 250, 277, 337, 493, 521, 569, 653, 709, 914, 1009, 1018, 1037, 1385, 1465, 1553, 1597, 1618, 1754, 1781, 1898, 1921, 1973, 1994, 2069, 2129, 2146, 2293, 2378, 2389, 2441, 2474, 2561, 2725, 2741, 2777, 2897, 2957, 2986, 3170, 3229, 3265
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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n = 1; t = {}; While[Length[t] < 60, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 3, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 03 2014 *)
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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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