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%I #14 Aug 10 2023 13:21:32
%S 11261,21953,22549,36181,36562,37330,53945,54877,55817,132058,165197,
%T 166825,199357,235754,238673,240629,242593,243578,277301,283649,
%U 284714,285781,287921,337129,372941,377837,426065,427370,428677,431297
%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 42.
%t cf42Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,2},ContinuedFraction[s][[2]]];len= Length[ cf];OddQ[len]&&cf[[Floor[len/2]]]==cf[[Ceiling[len/2]]]==42]; Select[Range[ 450000],cf42Q] (* _Harvey P. Dale_, Aug 10 2023 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E First term 1765 removed by _Georg Fischer_, Jun 16 2019