

A306218


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


1



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
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OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..33.


FORMULA

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


EXAMPLE

(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.


PROG

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


CROSSREFS

Cf. A003657, A232932, A241482 (the real quadratic field case).
A045535 and A094841 are similar sequences.
Sequence in context: A312748 A312749 A136403 * A312750 A312751 A312752
Adjacent sequences: A306215 A306216 A306217 * A306219 A306220 A306221


KEYWORD

nonn


AUTHOR

Jianing Song, Jan 29 2019


EXTENSIONS

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


STATUS

approved



