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 A344409 Positive discriminants of orders with class number 3. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 28 10:23 EST 2022. Contains 358411 sequences. (Running on oeis4.)