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

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..56.

Example

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

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*)

Crossrefs

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

Sequence in context: A195063 A138290 A023057 * A197171 A062316 A079299

Adjacent sequences: A197124 A197125 A197126 * A197128 A197129 A197130

Keyword

nonn

Author

Artur Jasinski, Oct 10 2011

Status

approved