A350956 Maximal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, 5, 64, 1107, 160160, 5713367, 889747443, 62837596341, 11671262491586, 3090090680653053, 635672008069583520, 278356729040728193703

Offset: 0

Author

Stefano Spezia, Jan 27 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 64:
   [5    2    3]
   [2    5    2]
   [3    2    5]
a(4) = 1107:
   [3    2    7    5]
   [2    3    2    7]
   [7    2    3    2]
   [5    7    2    3]
a(5) = 160160:
   [ 5   11    2    3    7]
   [11    5   11    2    3]
   [ 2   11    5   11    2]
   [ 3    2   11    5   11]
   [ 7    3    2   11    5]
		

Links

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

Crossrefs

Cf. A350933, A350955 (minimal).

Programs

Python

from itertools import permutations
from sympy import Matrix, prime
def A350956(n): return max(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