OFFSET
1,1
COMMENTS
In other words, a(n) is the smallest even k such that Q(sqrt(-k/4)) has class number n; or 0 if no such k exists.
Conjecture 1: a(n) > 0 for all n.
Conjecture 2: If a(n) > 0 and A060649(2n) > 0, then we have a(n) > A060649(2n). This would imply that all terms in A225060 are odd.
Conjecture 3: There exists a positive constant c such that a(n) < c*A060649(2n) for all n.
LINKS
Jianing Song, Table of n, a(n) for n = 1..250
Eric Weisstein's World of Mathematics, Class Number.
EXAMPLE
The smallest even k such that h(-k) = 2 is k = 20, so a(1) = 20.
The smallest even k such that h(-k) = 4 is k = 56, so a(2) = 56.
The smallest even k such that h(-k) = 12 is k = 356, so a(6) = 356.
PROG
(PARI) a(n) = my(d=4); while(!isfundamental(-d) || qfbclassno(-d)!=2*n, d+=4); d
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, May 08 2021
STATUS
approved