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

1,1

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.

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.

Example

See examples in A317987.

Prog

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

Crossrefs

Cf. A003644, A133676.

Subsequence of A317987.

Sequence in context: A330219 A013658 A227735 * A165346 A268083 A063480

Adjacent sequences: A319980 A319981 A319982 * A319984 A319985 A319986

Keyword

nonn,fini

Author

Jianing Song, Oct 02 2018

Status

approved