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

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

1,1

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

Table of n, a(n) for n=1..25.

Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

Prog

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

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.

Sequence in context: A106312 A023679 A187773 * A107662 A256872 A276435

Adjacent sequences: A328822 A328823 A328824 * A328826 A328827 A328828

Keyword

nonn,more

Author

Jianing Song, Dec 05 2019

Status

approved