A351021 Minimal permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, 13, 166, 4009, 169469, 10949857, 1078348288, 138679521597, 24402542896843, 5348124003487173

Offset: 0

Author

Stefano Spezia, Jan 29 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 166:
    3    2    5
    2    3    2
    5    2    3
a(4) = 4009:
    3    2    5    7
    2    3    2    5
    5    2    3    2
    7    5    2    3
a(5) = 169469:
    5    2    3    7   11
    2    5    2    3    7
    3    2    5    2    3
    7    3    2    5    2
   11    7    3    2    5
		

Links

• Lucas A. Brown, A351021+2.sage
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A348891, A350939, A350955, A351022 (maximal).

Programs

Python

from itertools import permutations
from sympy import Matrix, prime
def A351021(n): return 1 if n == 0 else min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(prime(i) for i in range(1,n+1))) # Chai Wah Wu, Jan 31 2022

Extensions

a(9) and a(10) from Lucas A. Brown, Sep 04 2022