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A005472
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Class numbers of cubic fields.
(Formerly M3291)
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2
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1, 1, 1, 1, 1, 1, 1, 4, 7, 4, 4, 4, 7, 4, 13, 7, 19, 7, 7, 7, 19, 19, 19, 16, 31, 19, 28, 19, 49, 31, 28, 31, 64, 43, 37, 127, 61, 52, 52, 52, 49, 100, 37, 112, 64, 67, 61, 76, 61, 76, 61, 61, 112, 76, 73, 67, 133, 91, 223, 169, 73, 112, 100, 169, 91, 121, 175
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OFFSET
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1,8
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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).
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PROG
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(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 */
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CROSSREFS
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Sequence in context: A020803 A019626 A203137 * A111522 A342203 A019735
Adjacent sequences: A005469 A005470 A005471 * A005473 A005474 A005475
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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