Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Mar 31 2019 02:20:27
%S 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,
%T 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,
%U 5,3,2,2,2,3,2,2,2,3,2,2,2,2,5,2,3,2,2,2
%N The least prime q such that Kronecker(D/q) >= 0 where D runs through all positive fundamental discriminants (A003658).
%C a(n) is the least prime that either decomposes or ramifies in the real quadratic field with discriminant D, D = A003658(n).
%C 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)).
%e 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.
%o (PARI) b(D)=forprime(p=2, oo, if(kronecker(D, p)>=0, return(p)))
%o for(n=1, 300, if(isfundamental(n), print1(b(n), ", ")))
%Y Cf. A003658.
%Y 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).
%K nonn
%O 1,1
%A _Jianing Song_, Feb 22 2019