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A094613 Fundamental discriminants of real quadratic number fields with class number 4.

%I A094613 #16 Feb 16 2025 08:32:53
%S A094613 145,328,445,505,520,680,689,777,780,793,840,876,897,901,905,924,1020,
%T A094613 1045,1096,1105,1145,1160,1164,1221,1288,1292,1313,1320,1365,1480,
%U A094613 1560,1640,1677,1736,1740,1745,1752,1820,1848,1885,1932,2005,2040,2056,2120,2145
%N A094613 Fundamental discriminants of real quadratic number fields with class number 4.
%H A094613 G. C. Greubel, <a href="/A094613/b094613.txt">Table of n, a(n) for n = 1..1000</a>
%H A094613 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A094613 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A094613 Select[Range[2145], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 4 &] (* _Arkadiusz Wesolowski_, Oct 22 2012 *)
%o A094613 (PARI) {ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==4};
%o A094613 for(n=1, 2500, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019
%o A094613 (Sage)
%o A094613 is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 4;
%o A094613 A094613 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
%o A094613 A094613(2500) # _G. C. Greubel_, Mar 01 2019
%Y A094613 Cf. A003656, A094619, A094612, A094614, A218156-A218160.
%K A094613 nonn
%O A094613 1,1
%A A094613 _Eric W. Weisstein_, May 14 2004