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%I #19 Feb 14 2021 13:06:00
%S 7,5,2,3,3,2,5,3,2,5,2,3,2,7,11,2,5,7,2,3,3,17,3,2,2,3,5,2,13,5,2,2,3,
%T 3,2,7,3,2,11,11,2,3,7,5,5,2,19,2,3,3,2,41,3,2,13,3,2,5,7,2,7,2,3,5,3,
%U 2,5,2,3,11,2,31,13,2,5,2,3,3,2,5,3,2,5,23,2,5,17,7,2,5,7,2,3,3
%N The least prime q such that Kronecker(D/q) = 1 where D runs through all negative fundamental discriminants (-A003657).
%C a(n) is the least prime that decomposes in the imaginary quadratic field with discriminant D, D = -A003657(n).
%C For most n, a(n) is relatively small. There are only 472 n's among [1, 3043] (there are 3043 terms in A003657 below 10000) that violate a(n) < log(A003657(n)).
%C Also a(n) is the smallest prime p such that the imaginary quadratic field with discriminant D = -A003657(n) can be embedded into the p-adic field Q_p. - _Jianing Song_, Feb 14 2021
%e Let K = Q[sqrt(-177)] with D = -708 = -A003657(218), we have: 2 and 3 divides 708, (-708/5) = (-708/7) = ... = (-708/29) = -1 and (-708/31) = +1, so 2 and 3 ramify in K, 5, 7, ..., 29 remain inert in K and 31 decomposes in K, so a(218) = 31.
%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. A003657.
%Y Similar sequences: A232931, A232932 (the least prime that remains inert); A306537, this sequence (the least prime that decomposes); A306541, A306542 (the least prime that decomposes or ramifies).
%K nonn
%O 1,1
%A _Jianing Song_, Feb 22 2019
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