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

4, 8, 15, 20, 24, 231, 264, 831, 920, 1364, 1364, 9044, 67044, 67044, 67044, 67044, 268719, 268719, 3604695, 4588724, 5053620, 5053620, 5053620, 5053620, 60369855, 364461096, 532735220, 715236599, 1093026360, 2710139064, 2710139064, 3356929784, 3356929784

Offset: 1

Author

Jianing Song, Jan 29 2019

Keywords

• nonn

Comments

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.

Examples

			(-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.
		

Crossrefs

Cf. A003657, A232932, A241482 (the real quadratic field case).

A045535 and A094841 are similar sequences.

Programs

PARI

a(n) = my(i=1); while(!isfundamental(-i)||sum(j=1, n, kronecker(-i,prime(j))==-1)!=0, i++); i

Formula

a(n) = A003657(k), where k is the smallest number such that A232932(k) >= prime(n+1).

Extensions

a(26)-a(33) from Jinyuan Wang, Apr 06 2019