cp's OEIS Frontend

A357573 Largest even k such that h(-k) = 2n, where h(D) is the class number of the quadratic field with discriminant D; or 0 if no such k exists.

%I A357573 #5 Oct 06 2022 14:43:09
%S A357573 232,1012,1588,3448,5272,8248,9172,14008,21652,21508,26548,32008,
%T A357573 45208,53188,57688,65668,73588,85012,121972,120712,117748,137272,
%U A357573 189352,162628,174868,201268,194968,249208,188248,332872,341608,424708,370792,411832,377512,539092,332308,486088,369832,435268,604948,667192,548788,601528,596212,566008,737752,795832,645208,802888
%N A357573 Largest even k such that h(-k) = 2n, where h(D) is the class number of the quadratic field with discriminant D; or 0 if no such k exists.
%C A357573 By definition, a(n) <= 4*A038552(2n).
%C A357573 Conjecture: if A038552(2n) == 3 (mod 4), a(n) > 0, then a(n) < A038552(2n). If this is true, then A038552(n) is also the largest absolute value of negative fundamental discriminant d for class number n.
%e A357573 a(1) = 232: h(-k) = 2 <=> k = 15, 20, 24, 35, 40, 51, 52, 88, 91, 115, 123, 148, 187, 232, 235, 267, 403, 427, so the largest even k such that h(-k) = 2 is k = 232.
%Y A357573 Cf. A038552, A344072.
%K A357573 nonn,hard
%O A357573 1,1
%A A357573 _Jianing Song_, Oct 03 2022