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A094612 Fundamental discriminants of real quadratic number fields with class number 3.

%I A094612 #22 Feb 16 2025 08:32:53
%S A094612 229,257,316,321,469,473,568,733,761,892,993,1016,1101,1229,1257,1304,
%T A094612 1373,1436,1489,1509,1772,1901,1929,1957,2021,2089,2101,2177,2213,
%U A094612 2429,2557,2589,2636,2677,2713,2777,2857,2917,2981,3173,3221,3229,3261,3356,3569
%N A094612 Fundamental discriminants of real quadratic number fields with class number 3.
%H A094612 G. C. Greubel, <a href="/A094612/b094612.txt">Table of n, a(n) for n = 1..1000</a>
%H A094612 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A094612 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A094612 Select[Range[3569], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 3 &] (* _Arkadiusz Wesolowski_, Oct 22 2012 *)
%o A094612 (PARI) {ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==3};
%o A094612 for(n=1, 3600, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019
%o A094612 (Sage)
%o A094612 is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 3;
%o A094612 A094612 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
%o A094612 A094612(3700) # _G. C. Greubel_, Mar 01 2019
%Y A094612 Cf. A003656, A094619, A094613-A094614, A218156-A218160.
%K A094612 nonn
%O A094612 1,1
%A A094612 _Eric W. Weisstein_, May 14 2004
%E A094612 Edited by _N. J. A. Sloane_, May 01 2010