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A306541
The least prime q such that Kronecker(D/q) >= 0 where D runs through all positive fundamental discriminants (A003658).
3
2, 5, 2, 2, 3, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 7, 2, 2, 2, 3, 2, 3, 2, 2, 7, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 3, 2, 2, 13, 2, 3, 2, 2, 2, 2, 7, 2, 2, 3, 2, 3, 2, 2, 5, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2
OFFSET
1,1
COMMENTS
a(n) is the least prime that either decomposes or ramifies in the real quadratic field with discriminant D, D = A003658(n).
For most n, a(n) is relatively small. There are only 86 n's among [1, 3044] (there are 3044 terms in A003658 below 10000) that violate a(n) < log(A003658(n)).
EXAMPLE
Let K = Q[sqrt(293)] with D = 293 = A003658(90), we have: (293/2) = (293/3) = ... = (293/13) = -1 and (293/17) = +1, so 2, 3, 5, 7, 11 and 13 remain inert in K and 17 decomposes in K, so a(90) = 17.
PROG
(PARI) b(D)=forprime(p=2, oo, if(kronecker(D, p)>=0, return(p)))
for(n=1, 300, if(isfundamental(n), print1(b(n), ", ")))
CROSSREFS
Cf. A003658.
Similar sequences: A232931, A232932 (the least prime that remains inert); A306537, A306538 (the least prime that decomposes); this sequence, A306542 (the least prime that decomposes or ramifies).
Sequence in context: A152765 A327867 A286664 * A242242 A171937 A065291
KEYWORD
nonn
AUTHOR
Jianing Song, Feb 22 2019
STATUS
approved