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A031543
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that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 45.
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0
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2027, 2039, 2047, 2063, 2083, 2087, 2091, 2099, 2111, 2123, 2131, 2143, 2147, 2179, 2187, 2191, 2203, 2207, 8104, 8168, 8192, 8200, 8256, 8296, 8320, 8352, 8384, 8448, 8480, 8488, 8512, 8544, 8552, 8576, 8584, 8608, 8704, 8736, 8744, 8800, 8832, 18231
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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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cf45Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]]==45]; Select[Range[20000], cf45Q] (* Harvey P. Dale, Dec 04 2022 *)
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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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