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

1,1

Comments

Numbers which occured in A172000 and not in A197115.

Links

Table of n, a(n) for n=1..54.

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

Crossrefs

Cf. A087643, A172000, A194366, A197115.

Sequence in context: A184825 A190372 A184837 * A319449 A030374 A369021

Adjacent sequences: A197117 A197118 A197119 * A197121 A197122 A197123

Keyword

nonn

Author

Artur Jasinski, Oct 10 2011

Status

approved