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%I #23 Aug 28 2020 01:52:22
%S 2,5,8,10,13,17,18,20,26,29,32,37,40,41,45,50,52,53,58,61,65,68,72,73,
%T 74,80,82,85,89,90,97,98,101,104,106,109,113,116,117,122,125,128,130,
%U 137,145,148,149,153,157,160,162,164,170,173,180,181,185,193,197,200
%N Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm -1.
%C Complement of A087643 in the nonsquare integers A000037.
%C Subsequence of A000415, their set difference form A172001.
%C Contains A003814 as a subsequence, their squarefree terms coincide and form A003654.
%C It seems that this sequence also gives the values of n such that the equation x^2 - n*y^2 = n has integer solutions. - _Colin Barker_, Aug 20 2013
%F A positive integer n is in this sequence iff its squarefree core A007913(n) belongs to A003654.
%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 *)
%o (PARI) { for(n=1,1000, if(issquare(n),next); if( norm(bnfinit(x^2-n).fu[1])==-1, print1(n,", ")) ) }
%K nonn
%O 1,1
%A _Max Alekseyev_, Jan 21 2010
%E Edited by _Max Alekseyev_, Mar 09 2010
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