OFFSET
1,8
COMMENTS
Class numbers of cubic fields with discriminants p^2, where p runs through the primes in A005471.
All terms are of the form x^2 + 3*y^2 (A003136). - Colin Barker, Nov 30 2014
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..100
D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 1137-1152 (see Table 1 page 1140).
PROG
(PARI) A175282(n)={
local(a);
if(n==1,
return(1),
a=A175282(n-1)+1;
while(1,
if( isprime(a^2+3*a+9),
return(a),
a++
);
)
)
};
A005472(n)={
local(a, bnf, L, H);
if(n==1, return(1));
a=A175282(n);
bnf=bnfinit(x^3-a*x^2-(a+3)*x-1);
L=ideallist(bnf, 1, 2);
H=bnrclassnolist(bnf, L);
return(H[1][1]);
};
for(n=1, 80, print1(A005472(n), " ") ); /* R. J. Mathar, Jun 06 2019 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved