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 A031676 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 88. 0
 96149, 160081, 238265, 334253, 438469, 441121, 445114, 562789, 565793, 705961, 709325, 712697, 1036853, 1040929, 1045013, 1212826, 1215029, 1219441, 1223861, 1230506, 1237169, 1416829, 1639241, 1644365, 1659785, 1664941, 1875122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..27. EXAMPLE The c.f. expansion of sqrt(96149) is 310, [12, 1, 1, 1, 8, 1, 1, 2, 21, 1, 3, 21, 1, 8, 1, 1, 2, 2, 2, 2, 1, 3, 154, 1, 3, 2, 1, 10, 1, 1, 2, 1, 1, 88, 88, 1, 1, 2, 1, 1, 10, 1, 2, 3, 1, 154, 3, 1, 2, 2, 2, 2, 1, 1, 8, 1, 21, 3, 1, 21, 2, 1, 1, 8, 1, 1, 1, 12, 620], [12, 1, 1, 1, 8, 1, 1, 2, 21, 1, 3, 21, 1, 8, 1, 1, 2, 2, 2, 2, 1, 3, 154, 1, 3, 2, 1, 10, 1, 1, 2, 1, 1, 88, 88, 1, 1, 2, 1, 1, 10, 1, 2, 3, 1, 154, 3, 1, 2, 2, 2, 2, 1, 1, 8, 1, 21, 3, 1, 21, 2, 1, 1, 8, 1, 1, 1, 12, 620], ..., where two copies of the period are shown. If the term 620 is deleted, the two central terms of the period are 88. So 96149 is a term. - N. J. A. Sloane, Aug 18 2021 MATHEMATICA cf88Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[s][[2]]]; len=Length[cf]; OddQ[len] && cf[[(len+1)/2]] == 88]; Select[Range[1875200], cf88Q] (* Harvey P. Dale, Aug 17 2021 *) CROSSREFS Sequence in context: A116265 A270149 A270116 * A205613 A205351 A343282 Adjacent sequences: A031673 A031674 A031675 * A031677 A031678 A031679 KEYWORD nonn AUTHOR David W. Wilson EXTENSIONS First term 7745 removed by Georg Fischer, Jun 16 2019 Name clarified by N. J. A. Sloane, Aug 18 2021 STATUS approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)