cp's OEIS Frontend

A094614 Fundamental discriminants of real quadratic number fields with class number 5.

%I A094614 #16 Feb 16 2025 08:32:53
%S A094614 401,817,1093,1393,1429,1641,1756,1897,1996,2081,2153,2908,3121,3181,
%T A094614 3253,3928,3997,4353,4357,4441,4504,4757,4889,5241,5269,5308,5944,
%U A094614 6113,6157,6481,6949,7064,7229,7513,7817,7861,8049,8108,8121,8309,8501,8689,9181,9229
%N A094614 Fundamental discriminants of real quadratic number fields with class number 5.
%H A094614 G. C. Greubel, <a href="/A094614/b094614.txt">Table of n, a(n) for n = 1..1000</a>
%H A094614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A094614 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A094614 Select[Range[9229], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 5 &] (* _Arkadiusz Wesolowski_, Oct 22 2012 *)
%o A094614 (PARI) {ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==5};
%o A094614 for(n=1, 10000, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019
%o A094614 (Sage)
%o A094614 is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 5;
%o A094614 A094614 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
%o A094614 A094614(10000) # _G. C. Greubel_, Mar 01 2019
%Y A094614 Cf. A003656, A094619, A094612-A094613, A218156-A218160.
%K A094614 nonn
%O A094614 1,1
%A A094614 _Eric W. Weisstein_, May 14 2004