A046008 - OEIS

%I #26 Mar 15 2019 22:51:58

%S 167,271,659,967,1283,1303,1307,1459,1531,1699,2027,2267,2539,2731,

%T 2851,2971,3203,3347,3499,3739,3931,4051,5179,5683,6163,6547,7027,

%U 7507,7603,7867,8443,9283,9403,9643,9787,10987,13003,13267,14107,14683,15667

%N Discriminants of imaginary quadratic fields with class number 11 (negated).

%H Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998) 295-330.

%H Duncan A. Buell, <a href="https://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.

%H Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>

%H C. Wagner, <a href="https://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Reap[ For[n = 1, n < 15000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 11, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* _Jean-François Alcover_, Oct 05 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 11};

%o for(n=1, 16000, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019

%o (Sage) [n for n in (1..16000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==11] # _G. C. Greubel_, Mar 01 2019

%Y Cf. A006203, A013658, A014602, A014603, A046002-A046020.

%Y Cf. A191410.

%K nonn,fini,full

%O 1,1

%A _Eric W. Weisstein_

%E a(40)-a(41) from _Giovanni Resta_, Mar 20 2013