A197121 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.

21, 69, 77, 84, 93, 133, 165, 189, 205, 213, 221, 237, 253, 276, 285, 301, 308, 309, 336, 341, 357, 372, 413, 429, 437, 453, 469, 501, 517, 525, 532, 581, 589, 597, 621, 645, 660, 669, 693, 717, 741, 749, 756, 789, 805, 820, 837, 852, 861, 869, 884, 893, 917

Offset

1,1

Comments

Numbers which occured in A087643 and not in A194366.

Links

Table of n, a(n) for n=1..53.

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: A123779 A123839 A180758 * A175461 A272627 A043339

Adjacent sequences: A197118 A197119 A197120 * A197122 A197123 A197124

Keyword

nonn

Author

Artur Jasinski, Oct 10 2011

Status

approved