A344409 Positive discriminants of orders with class number 3.

148, 229, 257, 316, 321, 404, 469, 473, 564, 568, 592, 621, 733, 756, 761, 788, 837, 892, 916, 993, 1016, 1028, 1076, 1101, 1229, 1257, 1264, 1284, 1304, 1332, 1373, 1396, 1436, 1489, 1492, 1509, 1524, 1556, 1573, 1593, 1616, 1620, 1772, 1876, 1892, 1901, 1929, 1944

Offset: 1

Author

Jianing Song, May 17 2021

Keywords

• nonn

Comments

Also positive discriminants of orders with class group isomorphic to C_3.

The fundamental terms are listed in A094612.

It seems that for most k in this sequence, 4*k is also in this sequence. The smallest k such that this is not true is k = 564.

Conjecture: if a term k is congruent to 4 modulo 16, then k/4 is either here or in A133315; if a term k is congruent to 0 modulo 16, then k/4 is in this sequence.

Conjecture: a term k is in A006832 if and only if k/4 is not in this sequence.

Links

• Jianing Song, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A133315 (positive discriminants of orders with class number 1), A344408 (class number 2), this sequence (class number 3).

Cf. A328825 (the negative discriminant case), A094612, A006832.

Programs

PARI

isA344409(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[3]