

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
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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.


LINKS



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



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



