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A225365 Negative fundamental discriminants with non-isomorphic class groups (negated).

%I A225365 #16 Dec 26 2015 02:21:26
%S A225365 3,15,23,39,47,71,84,87,95,119,167,191,199,215,231,239,260,311,327,
%T A225365 335,383,399,407,420,431,455,479,551,591,647,671,695,719,759,776,791,
%U A225365 831,839,887,935,959,983,1031,1079,1140,1151,1199,1239,1271,1295,1319,1391,1439,1487,1511,1559,1679,1751,1799,1847,1959,1991,2015
%N A225365 Negative fundamental discriminants with non-isomorphic class groups (negated).
%C A225365 More precisely, the least absolute values of negative fundamental discriminants with class groups non-isomorphic to all class groups for negative fundamental discriminants with smaller absolute values.
%C A225365 The n-th line of the linked file gives the invariant factor decomposition of the class group corresponding to the fundamental discriminant -a(n).
%H A225365 Rick L. Shepherd and Charles R Greathouse IV, <a href="/A225365/b225365.txt">Table of n, a(n) for n = 1..10000</a> (first 7194 terms from Shepherd)
%H A225365 Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
%H A225365 Rick L. Shepherd, <a href="/A225365/a225365.txt">Invariant factor decompositions for corresponding class groups</a>
%e A225365 The fundamental discriminant -3 corresponds to the trivial class group. The fundamental discriminant -15 is the first negative fundamental discriminant encountered (least absolute value) whose class group has a different structure, isomorphic to Z_2. The fundamental discriminant -84 is the one with least absolute value whose class group is isomorphic to the Klein-4 group.
%o A225365 (PARI)
%o A225365 {allocatemem(32000000);
%o A225365 \\ Increase precision to more than 100 digits to go beyond 7194 terms.
%o A225365 default(realprecision, 100);
%o A225365 terms_wanted = 7194;
%o A225365 G = Set(); k = 0;
%o A225365 while(length(G)<terms_wanted,
%o A225365   k++;
%o A225365   if(isfundamental(-k),
%o A225365     F = bnfinit(quadpoly(-k,x), , [6,6,4]); \\ Without optional 3rd argument, Generalized Riemann Hypothesis assumed
%o A225365     if(bnfcertify(F)<>1, print("Certify failed for ", -k, " -- exiting (", length(G), " terms found)"); break);
%o A225365     if(setsearch(G, F.clgp.cyc)==0,
%o A225365       G = setunion(G, [F.clgp.cyc]);
%o A225365       write("b225365.txt", length(G), " ", k);
%o A225365       write("a225365.txt", length(G), " ", F.clgp.cyc);
%o A225365       if(length(G)%100==0, print1("...", length(G), "... ")))))}
%Y A225365 Cf. A003657.
%K A225365 nonn
%O A225365 1,1
%A A225365 _Rick L. Shepherd_, May 05 2013