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

1,1

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

Prog

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

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.

Sequence in context: A061154 A252690 A134212 * A127028 A186894 A233727

Adjacent sequences: A344406 A344407 A344408 * A344410 A344411 A344412

Keyword

nonn

Author

Jianing Song, May 17 2021

Status

approved