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 A197115 Nonsquare positive integers k such that the fundamental unit of the quadratic field Q(sqrt(k)) has norm -1 and can be written as x + y*sqrt(d) with integers x, y where d is the squarefree part of k. 8
 2, 8, 10, 17, 18, 26, 32, 37, 40, 41, 50, 58, 65, 68, 72, 73, 74, 82, 89, 90, 97, 98, 101, 104, 106, 113, 122, 128, 130, 137, 145, 148, 153, 160, 162, 164, 170, 185, 193, 197, 200, 202, 218, 226, 232, 233, 234, 241, 242, 250, 257, 260, 265, 269, 272, 274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a subsequence of A172000. LINKS Table of n, a(n) for n=1..56. MATHEMATICA cr = {}; Do[If[IntegerQ[Sqrt[n]], , kk = NumberFieldFundamentalUnits[Sqrt[n]]; d1 = kk[[1]][[2]][[1]]; d2 = kk[[1]][[1]] kk[[1]][[2]][[2]]; d3 = Expand[(d1 + d2) (d1 - d2)]; If[d3 == -1, k1 = Max[Denominator[d1], Denominator[d2]]; If[k1 == 1, AppendTo[cr, n]]]], {n, 2, 400}]; cr CROSSREFS Cf. A087643, A172000, A194366. Sequence in context: A110913 A038638 A226831 * A288824 A190042 A297293 Adjacent sequences: A197112 A197113 A197114 * A197116 A197117 A197118 KEYWORD nonn AUTHOR Artur Jasinski, Oct 10 2011 EXTENSIONS Definition clarified by Emmanuel Vantieghem, Mar 06 2017 STATUS approved

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Last modified September 10 06:17 EDT 2024. Contains 375773 sequences. (Running on oeis4.)