cp's OEIS Frontend

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.

%I A197115 #17 Sep 04 2023 15:48:50
%S A197115 2,8,10,17,18,26,32,37,40,41,50,58,65,68,72,73,74,82,89,90,97,98,101,
%T A197115 104,106,113,122,128,130,137,145,148,153,160,162,164,170,185,193,197,
%U A197115 200,202,218,226,232,233,234,241,242,250,257,260,265,269,272,274
%N 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.
%C A197115 This sequence is a subsequence of A172000.
%t A197115 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
%Y A197115 Cf. A087643, A172000, A194366.
%K A197115 nonn
%O A197115 1,1
%A A197115 _Artur Jasinski_, Oct 10 2011
%E A197115 Definition clarified by _Emmanuel Vantieghem_, Mar 06 2017