A319983 Discriminants of imaginary quadratic fields with 2 classes per genus, negated.

39, 55, 56, 68, 136, 155, 184, 203, 219, 259, 260, 264, 276, 291, 292, 308, 323, 328, 355, 388, 456, 552, 564, 568, 580, 616, 651, 667, 723, 763, 772, 820, 852, 868, 915, 952, 955, 987, 1003, 1027, 1032, 1060, 1128, 1131, 1140, 1204, 1227, 1240, 1243, 1288, 1387, 1411, 1443

Offset: 1

Author

Jianing Song, Oct 02 2018

Keywords

• nonn
• fini

Comments

Fundamental terms of A317987.

k is a term iff the class group of Q[sqrt(-k)], or the form class group of positive binary quadratic forms with discriminant -k is isomorphic to (C_2)^r X C_4.

This is a subsequence of A133676, so it's finite. It seems that this sequence has 161 terms, the largest being 40755.

Examples

			See examples in A317987.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..161
• Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

Crossrefs

Cf. A003644, A133676.

Subsequence of A317987.

Programs

PARI

isA319983(n) = isfundamental(-n) && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]