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%I #26 Feb 17 2019 03:56:14
%S 8,12,24,60,60,364,984,1596,1596,1596,3705,58444,84396,164620,172236,
%T 369105,369105,731676,731676,3442296,3442296,32169916,32169916,
%U 47973864,47973864,47973864,313114620,313114620,313114620,313114620,13461106065,27765196680,40527839121,55213498824,55213498824,381031123720
%N Least fundamental discriminant D > 1 such that the first n primes p have (D/p) >= 0.
%C By the Chinese Remainder Theorem and Prime Number Theorem in arithmetic progressions, this sequence is infinite.
%C a(n) is the least fundamental discriminant D > 1 such that the first n primes either decompose or ramify in the real quadratic field with discriminant D. See A306218 for the imaginary quadratic field case. - _Jianing Song_, Feb 14 2019
%F a(n) > prime(n)^(4*sqrt(e) + o(1)). - _Charles R Greathouse IV_, Apr 23 2014
%F a(n) = A003658(k), where k is the smallest number such that A232931(k) >= prime(n+1). - _Jianing Song_, Feb 15 2019
%e (364/2) = 0, (364/3) = 1, (364/5) = 1, (364/7) = 0, (364/11) = 1, (364/13) = 0, so 3, 5, 11 decompose in Q[sqrt(91)] and 2, 7, 13 ramify in Q[sqrt(-231)]. For other fundamental discriminants 1 < D < 364, at least one of 2, 3, 5, 7, 11, 13 is inert in the imaginary quadratic field with discriminant D, so a(6) = 364. - _Jianing Song_, Feb 14 2019
%o (PARI) a(n) = my(i=2); while(!isfundamental(i)||sum(j=1, n, kronecker(i,prime(j))==-1)!=0, i++); i \\ _Jianing Song_, Feb 14 2019
%Y Cf. A003658, A232931, A306218 (the imaginary quadratic field case).
%Y A002189 and A094847 are similar sequences.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Apr 23 2014
%E a(36) from _Charles R Greathouse IV_, Apr 24 2014
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