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 A031543 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..42. MATHEMATICA 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 *) CROSSREFS Sequence in context: A350869 A031768 A156856 * A031723 A145721 A103126 Adjacent sequences: A031540 A031541 A031542 * A031544 A031545 A031546 KEYWORD nonn AUTHOR David W. Wilson STATUS approved

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Last modified February 27 16:21 EST 2024. Contains 370378 sequences. (Running on oeis4.)