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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
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
KEYWORD
nonn
AUTHOR
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.)