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Numbers k such 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 31.

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`%I #16 Jul 06 2024 15:59:27
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`%S 963,967,971,983,991,1003,1019,1031,1039,1051,1059,1063,1087,3848,
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`%T 3880,3904,3936,3944,4000,4040,4072,4168,4192,4256,4264,4288,4320,
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`%U 4328,4352,8655,8727,8787,8871,8943,9003,9147,9303,9375,9663,9795,15384,15448
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`%N Numbers k such 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 31.
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`%t epct31Q[n_]:=Module[{cf=ContinuedFraction[Sqrt[n]],cf2},If[Length[cf] ==1, cf2={1},cf2=cf[[2]]];EvenQ[Length[ cf2]] && cf2[[Length[cf2]/2]] == 31]; Select[ Range[16000],epct31Q] (* _Harvey P. Dale_, Dec 07 2012 *)
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`%K nonn
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`%O 1,1
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`%A _David W. Wilson_
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