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A319983 Discriminants of imaginary quadratic fields with 2 classes per genus, negated. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 14 04:39 EDT 2021. Contains 345018 sequences. (Running on oeis4.)