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A087643
Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) 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
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
Sequence in context: A051146 A136272 A101184 * A248150 A022544 A194366
KEYWORD
easy,nonn
AUTHOR
Thomas Baruchel, Sep 16 2003
EXTENSIONS
Edited by Max Alekseyev, May 03 2010
STATUS
approved