|
| |
|
|
A087643
|
|
Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(d)) has norm 1.
|
|
13
| |
|
|
3, 6, 7, 11, 12, 14, 15, 19, 21, 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, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,1
|
|
|
COMMENTS
| No quadratic number with a fully periodical continued fraction of period 1 can be written as (a+b*sqrt(n))/c with n allowed to have square factors.
Subsequence of the squarefree terms is A087642.
|
|
|
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, AppendTo[cr, n]]], {n, 2, 1000}]; cr (* Artur Jasinski, Oct 10 2011 *)
|
|
|
CROSSREFS
| Cf. A087642, A172000.
Sequence in context: A051146 A136272 A101184 * A022544 A194366 A091067
Adjacent sequences: A087640 A087641 A087642 * A087644 A087645 A087646
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Thomas Baruchel (baruchel(AT)users.sourceforge.net), Sep 16 2003
|
|
|
EXTENSIONS
| Edited by Max Alekseyev (maxale(AT)gmail.com), May 03 2010
|
| |
|
|
