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A031409
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Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 6.
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1
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38, 46, 54, 62, 84, 93, 111, 129, 141, 148, 164, 172, 188, 204, 212, 230, 236, 244, 245, 252, 270, 295, 305, 330, 345, 355, 395, 426, 448, 469, 474, 497, 518, 553, 570, 581, 584, 602, 609, 616, 632, 644, 648, 658, 712, 721, 738, 742, 749, 763, 765, 777, 801
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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] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && c[[2, len/2]] == 6, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
cf6Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]]==6]; Select[Range[1000], cf6Q] (* Harvey P. Dale, Feb 04 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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