A348891 Minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, 5, 12, 11, 22, 84, 1368, 73, 589, 15057, 2520, 28209

Offset: 0

Author

N. J. A. Sloane and Stefano Spezia, Jan 28 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 12:
    2    3    5
    3    2    3
    5    3    2
a(4) = 11:
    2    5    3    7
    5    2    5    3
    3    5    2    5
    7    3    5    2
a(5) = 22:
    2    3    5    7   11
    3    2    3    5    7
    5    3    2    3    5
    7    5    3    2    3
   11    7    5    3    2
		

Links

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

Crossrefs

Cf. A350932, A350955.

Programs

Python

from itertools import permutations
from sympy import Matrix, prime
def A348891(n): return min(d for d in (abs(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))) if d > 0) # Chai Wah Wu, Jan 28 2022

Extensions

a(9) from Alois P. Heinz, Jan 28 2022

a(10)-a(12) from Lucas A. Brown, Aug 31 2022