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
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
Programs
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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