cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A306218 Fundamental discriminant D < 0 with the least absolute value such that the first n primes p have (D/p) >= 0, negated.

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%I A306218 #34 Apr 06 2019 10:57:10
%S A306218 4,8,15,20,24,231,264,831,920,1364,1364,9044,67044,67044,67044,67044,
%T A306218 268719,268719,3604695,4588724,5053620,5053620,5053620,5053620,
%U A306218 60369855,364461096,532735220,715236599,1093026360,2710139064,2710139064,3356929784,3356929784
%N A306218 Fundamental discriminant D < 0 with the least absolute value such that the first n primes p have (D/p) >= 0, negated.
%C A306218 a(n) is the negated fundamental discriminant D < 0 with the least absolute value such that the first n primes either decompose or ramify in the imaginary quadratic field with discriminant D. See A241482 for the real quadratic field case.
%F A306218 a(n) = A003657(k), where k is the smallest number such that A232932(k) >= prime(n+1).
%e A306218 (-231/2) = 1, (-231/3) = 0, (-231/5) = 1, (-231/7) = 0, (-231/11) = 0, (-231/13) = 1, so 2, 5, 13 decompose in Q[sqrt(-231)] and 3, 7, 11 ramify in Q[sqrt(-231)]. For other fundamental discriminants -231 < D < 0, at least one of 2, 3, 5, 7, 11, 13 is inert in the imaginary quadratic field with discriminant D, so a(6) = 231.
%o A306218 (PARI) a(n) = my(i=1); while(!isfundamental(-i)||sum(j=1, n, kronecker(-i,prime(j))==-1)!=0, i++); i
%Y A306218 Cf. A003657, A232932, A241482 (the real quadratic field case).
%Y A306218 A045535 and A094841 are similar sequences.
%K A306218 nonn
%O A306218 1,1
%A A306218 _Jianing Song_, Jan 29 2019
%E A306218 a(26)-a(33) from _Jinyuan Wang_, Apr 06 2019