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.
%I A344409 #16 May 18 2021 04:07:38 %S A344409 148,229,257,316,321,404,469,473,564,568,592,621,733,756,761,788,837, %T A344409 892,916,993,1016,1028,1076,1101,1229,1257,1264,1284,1304,1332,1373, %U A344409 1396,1436,1489,1492,1509,1524,1556,1573,1593,1616,1620,1772,1876,1892,1901,1929,1944 %N A344409 Positive discriminants of orders with class number 3. %C A344409 Also positive discriminants of orders with class group isomorphic to C_3. %C A344409 The fundamental terms are listed in A094612. %C A344409 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. %C A344409 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. %C A344409 Conjecture: a term k is in A006832 if and only if k/4 is not in this sequence. %H A344409 Jianing Song, <a href="/A344409/b344409.txt">Table of n, a(n) for n = 1..10001</a> %o A344409 (PARI) isA344409(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[3] %Y A344409 Cf. A133315 (positive discriminants of orders with class number 1), A344408 (class number 2), this sequence (class number 3). %Y A344409 Cf. A328825 (the negative discriminant case), A094612, A006832. %K A344409 nonn %O A344409 1,1 %A A344409 _Jianing Song_, May 17 2021