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%I #42 May 17 2021 08:41:43
%S 23,31,44,59,76,83,92,107,108,124,139,172,211,243,268,283,307,331,379,
%T 499,547,643,652,883,907
%N Negative discriminants with form class group isomorphic to C_3 (negated).
%C Also negative discriminants with form class number 3.
%C Conjecture: this sequence is finite and this is the full list.
%C The fundamental terms are listed in A006203, and that is a full sequence.
%C From _Jianing Song_, May 17 2021: (Start)
%C Equivalently, negative discriminants of orders whose class group is isomorphic to C_3 (negated).
%C The known even terms are all congruent to 12 modulo 16. Among the known even terms, k/4 is either here or in A133675. What's the reason for that?
%C Among the known terms, k is in A023679 if and only if k is in this sequence and k/4 is not. Is there a connection between these two sequences? (End)
%H 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.
%o (PARI) isA328825(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[3] \\ Corrected by _Jianing Song_, May 17 2021
%Y Cf. A133675 (negative discriminants with form class group isomorphic to the trivial group), A322710 (isomorphic to C_2), this sequence (isomorphic to C_3), A329182 (isomorphic to C_2 X C_2), A330219 (isomorphic to C_4).
%Y Cf. A006203, A023679.
%K nonn,more
%O 1,1
%A _Jianing Song_, Dec 05 2019
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