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%I #21 Aug 28 2020 01:50:29
%S 3,6,7,11,12,14,15,19,21,22,23,24,27,28,30,31,33,34,35,38,39,42,43,44,
%T 46,47,48,51,54,55,56,57,59,60,62,63,66,67,69,70,71,75,76,77,78,79,83,
%U 84,86,87,88,91,92,93,94,95,96,99,102,103,105,107,108,110,111,112,114
%N Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1.
%C 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.
%C Subsequence of the squarefree terms is A087642.
%t 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 *)
%Y Cf. A087642, A172000.
%K easy,nonn
%O 3,1
%A _Thomas Baruchel_, Sep 16 2003
%E Edited by _Max Alekseyev_, May 03 2010
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