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

1, 2, -11, -286, -57935, -5696488, -1764195984, -521528189252

Offset: 0

Author

Stefano Spezia, Jan 25 2022

Keywords

• sign
• hard
• more

Examples

			a(2) = -11:
    2    3
    5    2
a(3) = -286:
    5    7    2
   11    5    7
    3   11    5
		

Links

• Lucas A. Brown, A350932+3.py
• Mathematics Stack Exchange, Why is the determinant of the 0 x 0 matrix equal 1?
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A318173, A350930, A350933 (maximal).

Programs

Maple

f:= proc(n) local i;
  min(map(t -> LinearAlgebra:-Determinant(LinearAlgebra:-ToeplitzMatrix(t)), combinat:-permute([seq(ithprime(i),i=1..2*n-1)]))) end proc:
f(0):= 1:
map(f, [$0..5]); # Robert Israel, Apr 01 2024

Python

from itertools import permutations
from sympy import Matrix, prime
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

Extensions

a(5) from Alois P. Heinz, Jan 25 2022

a(6)-a(7) from Lucas A. Brown, Aug 27 2022