A350955 - OEIS

%I #22 Oct 12 2022 05:31:52

%S 1,2,-5,-35,-435,-87986,-7186995,-496722800,-68316404507,

%T -9102428703537,-3721326642272925,-488684390484513105,

%U -195315251884652232704

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

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A348891%2BA350955%2B6.py">A348891+A350955+6.py</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

%e a(3) = -35:

%e    [3    5    2]

%e    [5    3    5]

%e    [2    5    3]

%e a(4) = -435:

%e    [5    7    2    3]

%e    [7    5    7    2]

%e    [2    7    5    7]

%e    [3    2    7    5]

%e a(5) = -87986:

%e    [ 2    3   11    5    7]

%e    [ 3    2    3   11    5]

%e    [11    3    2    3   11]

%e    [ 5   11    3    2    3]

%e    [ 7    5   11    3    2]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix, prime

%o 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

%Y Cf. A350932, A350956 (maximal), A348891.

%K sign,hard,more

%O 0,2

%A _Stefano Spezia_, Jan 27 2022

%E a(9) from _Alois P. Heinz_, Jan 27 2022

%E a(10)-a(12) from _Lucas A. Brown_, Aug 29 2022