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A350932 Minimal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers, with a(0) = 1.

%I A350932 #27 Apr 04 2024 10:21:36
%S A350932 1,2,-11,-286,-57935,-5696488,-1764195984,-521528189252
%N A350932 Minimal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers, with a(0) = 1.
%H A350932 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350932%2B3.py">A350932+3.py</a>
%H A350932 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/1762537/why-is-the-determinant-of-the-0x0-matrix-equal-1">Why is the determinant of the 0 x 0 matrix equal 1?</a>
%H A350932 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A350932 a(2) = -11:
%e A350932     2    3
%e A350932     5    2
%e A350932 a(3) = -286:
%e A350932     5    7    2
%e A350932    11    5    7
%e A350932     3   11    5
%p A350932 f:= proc(n) local i;
%p A350932   min(map(t -> LinearAlgebra:-Determinant(LinearAlgebra:-ToeplitzMatrix(t)), combinat:-permute([seq(ithprime(i),i=1..2*n-1)]))) end proc:
%p A350932 f(0):= 1:
%p A350932 map(f, [$0..5]); # _Robert Israel_, Apr 01 2024
%o A350932 (Python)
%o A350932 from itertools import permutations
%o A350932 from sympy import Matrix, prime
%o A350932 def A350932(n): return min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,2*n))) # _Chai Wah Wu_, Jan 27 2022
%Y A350932 Cf. A318173, A350930, A350933 (maximal).
%K A350932 sign,hard,more
%O A350932 0,2
%A A350932 _Stefano Spezia_, Jan 25 2022
%E A350932 a(5) from _Alois P. Heinz_, Jan 25 2022
%E A350932 a(6)-a(7) from _Lucas A. Brown_, Aug 27 2022