A197128 - OEIS

%I #16 Mar 02 2017 13:12:27

%S 2,3,5,7,8,10,11,12,13,15,17,18,19,20,21,23,24,26,27,28,29,31,32,33,

%T 35,37,39,40,41,43,44,45,47,48,50,51,52,53,55,57,58,59,60,61,63,65,67,

%U 68,71,72,73,74,75,76,77,79,80,82,83,84,85,88,89,90,91,92

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

%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

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 10 2011