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

6, 14, 22, 30, 34, 38, 42, 46, 54, 56, 62, 66, 69, 70, 78, 86, 87, 93, 94, 102, 110, 114, 115, 118, 126, 130, 132, 134, 138, 142, 146, 150, 154, 155, 156, 158, 159, 166, 174, 177, 178, 182, 183, 184, 185, 186, 190, 194, 198, 206, 210, 214, 220, 222, 228, 230

Offset: 1

Author

Artur Jasinski, Oct 10 2011

Keywords

• nonn

Comments

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

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

Examples

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

Crossrefs

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

Programs

Mathematica

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*)