A197120 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(d))has norm -1 and minimum one from two parts of fundamental unit are not integer.

5, 13, 20, 29, 45, 52, 53, 61, 80, 85, 109, 116, 117, 125, 149, 157, 173, 180, 181, 208, 212, 229, 244, 245, 261, 277, 293, 317, 320, 325, 340, 365, 397, 405, 421, 436, 445, 461, 464, 468, 477, 493, 500, 509, 533, 541, 549, 565, 596, 605, 613, 628, 629, 637

Offset: 1

Author

Artur Jasinski, Oct 10 2011

Keywords

• nonn

Comments

Numbers that occur in A172000 and not in A197115.

Crossrefs

Cf. A087643, A172000, A194366, A197115.

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]]; d3 = Expand[(d1 + d2) (d1 - d2)]; If[d3 == -1, k1 = Max[Denominator[d1], Denominator[d2]]; If[k1 == 1, , AppendTo[cr, n]]]], {n, 2, 2000}]; cr