A350955 Minimal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, -5, -35, -435, -87986, -7186995, -496722800, -68316404507, -9102428703537, -3721326642272925, -488684390484513105, -195315251884652232704

Offset: 0

Author

Stefano Spezia, Jan 27 2022

Keywords

• sign
• hard
• more

Examples

			a(3) = -35:
   [3    5    2]
   [5    3    5]
   [2    5    3]
a(4) = -435:
   [5    7    2    3]
   [7    5    7    2]
   [2    7    5    7]
   [3    2    7    5]
a(5) = -87986:
   [ 2    3   11    5    7]
   [ 3    2    3   11    5]
   [11    3    2    3   11]
   [ 5   11    3    2    3]
   [ 7    5   11    3    2]
		

Links

• Lucas A. Brown, A348891+A350955+6.py
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A350932, A350956 (maximal), A348891.

Programs

Python

from itertools import permutations
from sympy import Matrix, prime
def A350955(n): return min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,n+1))) # Chai Wah Wu, Jan 27 2022

Extensions

a(9) from Alois P. Heinz, Jan 27 2022

a(10)-a(12) from Lucas A. Brown, Aug 29 2022