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 A197127 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(d))is singular. 5

%I

%S 6,14,22,30,34,38,42,46,54,56,62,66,69,70,78,86,87,93,94,102,110,114,

%T 115,118,126,130,132,134,138,142,146,150,154,155,156,158,159,166,174,

%U 177,178,182,183,184,185,186,190,194,198,206,210,214,220,222,228,230

%N Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(d))is singular.

%C x^2+n*y^2=(+/-)2^s where s is 0 or 1.

%C Definition: Unity is singular when GCD[n,y]<>1.

%e a(1)=6 because unity of quadratic field Q(6) is 5+2*Sqrt[6] and GCD[2,6]=2 <>1.

%t cr = {}; 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[cr, n]]], {n, 2, 330}]; cr (*Artur Jasinski*)

%Y Cf. A087643, A172000, A194366, A197115, A197128.

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 10 2011

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Last modified March 28 05:13 EDT 2020. Contains 333073 sequences. (Running on oeis4.)