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 A225365 Negative fundamental discriminants with non-isomorphic class groups (negated). 2
 3, 15, 23, 39, 47, 71, 84, 87, 95, 119, 167, 191, 199, 215, 231, 239, 260, 311, 327, 335, 383, 399, 407, 420, 431, 455, 479, 551, 591, 647, 671, 695, 719, 759, 776, 791, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. The n-th line of the linked file gives the invariant factor decomposition of the class group corresponding to the fundamental discriminant -a(n). LINKS Rick L. Shepherd and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 7194 terms from Shepherd) Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013. Rick L. Shepherd, Invariant factor decompositions for corresponding class groups EXAMPLE 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. PROG (PARI) {allocatemem(32000000); \\ Increase precision to more than 100 digits to go beyond 7194 terms. default(realprecision, 100); terms_wanted = 7194; G = Set(); k = 0; while(length(G)1, print("Certify failed for ", -k, " -- exiting (", length(G), " terms found)"); break);     if(setsearch(G, F.clgp.cyc)==0,       G = setunion(G, [F.clgp.cyc]);       write("b225365.txt", length(G), " ", k);       write("a225365.txt", length(G), " ", F.clgp.cyc);       if(length(G)%100==0, print1("...", length(G), "... ")))))} CROSSREFS Cf. A003657. Sequence in context: A083934 A072200 A106403 * A225060 A060649 A344073 Adjacent sequences:  A225362 A225363 A225364 * A225366 A225367 A225368 KEYWORD nonn AUTHOR Rick L. Shepherd, May 05 2013 STATUS approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)