A197128 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n))is not singular.

2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 67, 68, 71, 72, 73, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 88, 89, 90, 91, 92

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..66.

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

Crossrefs

Cf. A087643, A172000, A194366, A197115, A197127.

Sequence in context: A302293 A266347 A028788 * A034707 A288378 A187909

Adjacent sequences: A197125 A197126 A197127 * A197129 A197130 A197131

Keyword

nonn

Author

Artur Jasinski, Oct 10 2011

Status

approved