%I #9 Apr 29 2021 12:06:30
%S 3,23,275,4511,9747,184607
%N Minimal absolute value of negative discriminants of number fields of degree n.
%C Conjecture: A343690(n) < a(n) for n == 0, 1 (mod 4), A343690(n) > a(n) for n == 2, 3 (mod 4).
%C 1257728 <= a(8) <= 4286875.
%H LMFDB, <a href="https://www.lmfdb.org/NumberField">Number fields</a>
%H A. M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/zeta.html">Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: A survey of recent results</a>, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141.
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%F A006557(n) = Min_{A343690(n), a(n)}.
%e The number field F of degree n whose discriminant is negative and of minimal absolute value:
%e n = 2, F = Q[x]/(x^2 - x + 1), d = -3;
%e n = 3, F = Q[x]/(x^3 - x^2 + 1), d = -23;
%e n = 4, F = Q[x]/(x^4 - x^3 + 2x - 1), d = -275;
%e n = 5, F = Q[x]/(x^5 - x^3 - 2x^2 + 1), d = -4511;
%e n = 6, F = Q[x]/(x^6 - x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1), d = -9747;
%e n = 7, F = Q[x]/(x^7 - x^6 - x^5 + x^4 - x^2 + x + 1), d = -184607.
%Y Cf. A343690 (the positive discriminant case), A006557 (the overall case).
%K nonn,hard,more
%O 2,1
%A _Jianing Song_, Apr 29 2021