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%I #17 Aug 18 2021 00:24:08
%S 96149,160081,238265,334253,438469,441121,445114,562789,565793,705961,
%T 709325,712697,1036853,1040929,1045013,1212826,1215029,1219441,
%U 1223861,1230506,1237169,1416829,1639241,1644365,1659785,1664941,1875122
%N 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.
%e 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
%t 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 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E First term 7745 removed by _Georg Fischer_, Jun 16 2019
%E Name clarified by _N. J. A. Sloane_, Aug 18 2021
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