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%I #12 Aug 02 2019 21:15:40
%S 6,14,22,30,34,38,42,54,56,62,66,86,94,102,110,118,126,132,134,138,
%T 142,146,150,156,158,166,174,178,182,186,190,194,198,206,210,214,220,
%U 222,228,230,246,254,258,262,270,278,282,286,294,302,306,310,322,326
%N Values k such that singular quadratic unity of Q(k) have gcd(k,y) = 2.
%C Conjecture: This sequence is infinite.
%t cr = {}; ck = {}; Do[If[IntegerQ[Sqrt[n]], , kk = NumberFieldFundamentalUnits[Sqrt[n]]; d1 = kk[[1]][[2]][[1]]; d2 = kk[[1]][[1]] kk[[1]][[2]][[2]]; d4 = Numerator[d2/Sqrt[n]]; If[GCD[d4, n] == 1, , AppendTo[ck, GCD[d4, n]]; AppendTo[cr, n]]], {n, 2, 200000}];aa = {}; Do[If[ck[[n]] == 2, AppendTo[aa, cr[[n]]]], {n, 1, Length[cr]}]; aa
%Y Cf. A087643, A172000, A194366, A197115, A197127, A197128, A197170.
%K nonn
%O 2,1
%A _Artur Jasinski_, Oct 11 2011
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