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 1-4 of 4 results.

A328825 Negative discriminants with form class group isomorphic to C_3 (negated).

Original entry on oeis.org

23, 31, 44, 59, 76, 83, 92, 107, 108, 124, 139, 172, 211, 243, 268, 283, 307, 331, 379, 499, 547, 643, 652, 883, 907
Offset: 1

Views

Author

Jianing Song, Dec 05 2019

Keywords

Comments

Also negative discriminants with form class number 3.
Conjecture: this sequence is finite and this is the full list.
The fundamental terms are listed in A006203, and that is a full sequence.
From Jianing Song, May 17 2021: (Start)
Equivalently, negative discriminants of orders whose class group is isomorphic to C_3 (negated).
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?
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)

Links

Crossrefs

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).
Cf. A006203, A023679.

Programs

  • PARI
    isA328825(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[3] \\ Corrected by Jianing Song, May 17 2021

A329182 Negative discriminants with form class group isomorphic to C_2 X C_2 (negated).

Original entry on oeis.org

84, 96, 120, 132, 160, 168, 180, 192, 195, 228, 240, 280, 288, 312, 315, 340, 352, 372, 408, 435, 448, 483, 520, 532, 555, 595, 627, 708, 715, 760, 795, 928, 1012, 1435
Offset: 1

Views

Author

Jianing Song, Dec 05 2019

Keywords

Comments

This sequence is finite and this is the full list.
Equivalently, negative discriminants of orders whose class group is isomorphic to C_2 X C_2 (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), this sequence (isomorphic to C_2 X C_2), A330219 (isomorphic to C_4).
The fundamental terms are listed in A192322. Cf. also A013658.

Programs

  • PARI
    isA329182(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[2,2] \\ Jianing Song, May 17 2021

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

A344408 Positive discriminants of orders with class number 2.

Original entry on oeis.org

40, 60, 65, 85, 96, 104, 105, 120, 136, 140, 156, 160, 165, 168, 185, 192, 200, 204, 205, 220, 221, 224, 232, 240, 252, 260, 264, 265, 273, 280, 285, 288, 296, 300, 305, 312, 320, 325, 336, 340, 345, 348, 352, 357, 360, 364, 365, 377, 380, 384, 385, 408
Offset: 1

Views

Author

Jianing Song, May 17 2021

Keywords

Comments

Also positive discriminants of orders with class group isomorphic to C_2.
The fundamental terms are listed in A094619.

Links

Crossrefs

Cf. A133315 (positive discriminants of orders with class number 1), this sequence (class number 2), A344409 (class number 3).
Cf. A322710 (the negative discriminant case), A094619.

Programs

  • PARI
    isA344408(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[2]
Showing 1-4 of 4 results.

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