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 A197171 Values k such that singular quadratic unity of Q(k) have gcd(k,y) = 2. 1
 6, 14, 22, 30, 34, 38, 42, 54, 56, 62, 66, 86, 94, 102, 110, 118, 126, 132, 134, 138, 142, 146, 150, 156, 158, 166, 174, 178, 182, 186, 190, 194, 198, 206, 210, 214, 220, 222, 228, 230, 246, 254, 258, 262, 270, 278, 282, 286, 294, 302, 306, 310, 322, 326 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Conjecture: This sequence is infinite. LINKS MATHEMATICA 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 CROSSREFS Cf. A087643, A172000, A194366, A197115, A197127, A197128, A197170. Sequence in context: A138290 A023057 A197127 * A062316 A079299 A043445 Adjacent sequences:  A197168 A197169 A197170 * A197172 A197173 A197174 KEYWORD nonn AUTHOR Artur Jasinski, Oct 11 2011 STATUS approved

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Last modified April 3 13:53 EDT 2020. Contains 333197 sequences. (Running on oeis4.)