cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A317987 Discriminants of orders of imaginary quadratic fields with 2 classes per genus, negated.

Original entry on oeis.org

39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 224, 252, 256, 259, 260, 264, 275, 276, 291, 292, 308, 320, 323, 328, 336, 355, 360, 363, 384, 387, 388, 400, 456, 468, 475, 504, 507, 528, 544, 552, 564, 568, 576, 580, 592, 600, 603, 612, 616, 624, 640
Offset: 1

Views

Author

Jianing Song, Oct 02 2018

Keywords

Comments

k is a term iff 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 324 terms, the largest being 87360.
The smallest number in A133676 but not here is 3600.

Links

Crossrefs

Cf. A003171, A133676.
Fundamental terms are listed in A319983.

Programs

  • PARI
    isA317987(n) = (-n)%4 < 2 && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]

Formula

The form class groups of positive binary quadratic forms with discriminant -39, -55, -56, -63, -68, -80 and -128 are all isomorphic to C_4, so 39, 55, 56, 63, 68, 80 and 128 are all members of this sequence.

A330219 Negative discriminants with form class group isomorphic to C_4 (negated).

Original entry on oeis.org

39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 252, 256, 259, 275, 291, 292, 323, 328, 355, 363, 387, 388, 400, 475, 507, 568, 592, 603, 667, 723, 763, 772, 955, 1003, 1027, 1227, 1243, 1387, 1411, 1467, 1507, 1555
Offset: 1

Views

Author

Jianing Song, Dec 05 2019

Keywords

Comments

It seems that this is the full list.
Equivalently, negative discriminants of orders whose class group is isomorphic to C_4 (negated). - Jianing Song, May 17 2021

Links

Crossrefs

Cf. A133675 (negative discriminants with form class group isomorphic to the trivial group), A322710 (isomorphic to C_2), A328825 (isomorphic to C_3), A329182 (isomorphic to C_2 X C_2), this sequence (isomorphic to C_4).
Subsequence of A133676 and A317987. Cf. also A013658.

Programs

  • PARI
    isA330219(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[4] \\ Jianing Song, May 17 2021

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

Original entry on oeis.org

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

Views

Author

Jianing Song, Oct 02 2018

Keywords

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

Crossrefs

Cf. A003644, A133676.
Subsequence of A317987.

Programs

  • PARI
    isA319983(n) = isfundamental(-n) && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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