|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This sequence is a subsequence of A087643.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|