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%I #34 May 09 2021 11:20:25
%S 3,6,7,11,12,14,15,19,22,23,24,27,28,30,31,33,34,35,38,39,42,43,44,46,
%T 47,48,51,54,55,56,57,59,60,62,63,66,67,70,71,75,76,78,79,83,86,87,88,
%U 91,92,94,95,96,99,102,103,105,107,108,110,111,112,114,115
%N Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1 and can be written as x+y*sqrt(d) with integers x, y where d is the squarefree part of n.
%C This sequence is a subsequence of A087643.
%e 35 belongs to this sequence because x^2 + 35*y^2 = 1 has the integer solution x=6, y=1.
%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, k1 = Max[Denominator[d1], Denominator[d2]]; If[k1 == 1, AppendTo[cr, n]]]], {n, 2, 100}]; cr
%Y Cf. A087643, A172000.
%K nonn
%O 1,1
%A _Artur Jasinski_, Oct 10 2011
%E Definition clarified by _Emmanuel Vantieghem_, Mar 06 2017
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