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

0,2

Links

Table of n, a(n) for n=0..7.

Lucas A. Brown, A350932+3.py

Mathematics Stack Exchange, Why is the determinant of the 0 x 0 matrix equal 1?

Wikipedia, Toeplitz Matrix

Example

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

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

Prog

(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

Crossrefs

Cf. A318173, A350930, A350933 (maximal).

Sequence in context: A248865 A072386 A185122 * A369947 A198894 A367798

Adjacent sequences: A350929 A350930 A350931 * A350933 A350934 A350935

Keyword

sign,hard,more

Author

Stefano Spezia, Jan 25 2022

Extensions

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

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

Status

approved