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A194366 revision #33

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.

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 subsequence of A087643.

LINKS

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

EXAMPLE

35 belongs to this sequence because x^2 + 35*y^2 = 1 has the 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

proposed