

A194366


Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1 and can be written as x+y*sqrt(d) with integers x, y where d is the squarefree part of n.


9



3, 6, 7, 11, 12, 14, 15, 19, 22, 23, 24, 27, 28, 30, 31, 33, 34, 35, 38, 39, 42, 43, 44, 46, 47, 48, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 70, 71, 75, 76, 78, 79, 83, 86, 87, 88, 91, 92, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114, 115
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OFFSET

1,1


COMMENTS

This sequence is a subset of A087643.


LINKS

Table of n, a(n) for n=1..63.


EXAMPLE

35 belong to this sequence because x^2+35*y^2=1 have integer solution: x=6, y=1.


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, 100}]; cr


CROSSREFS

Cf. A087643, A172000.
Sequence in context: A087643 A248150 A022544 * A091067 A269177 A269178
Adjacent sequences: A194363 A194364 A194365 * A194367 A194368 A194369


KEYWORD

nonn


AUTHOR

Artur Jasinski, Oct 10 2011


EXTENSIONS

Definition clarified by Emmanuel Vantieghem, Mar 06 2017


STATUS

approved



