A348891 - OEIS

%I #25 Oct 12 2022 08:24:28

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

%N Minimal absolute value of determinant of a nonsingular 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) = 12:

%e     2    3    5

%e     3    2    3

%e     5    3    2

%e a(4) = 11:

%e     2    5    3    7

%e     5    2    5    3

%e     3    5    2    5

%e     7    3    5    2

%e a(5) = 22:

%e     2    3    5    7   11

%e     3    2    3    5    7

%e     5    3    2    3    5

%e     7    5    3    2    3

%e    11    7    5    3    2

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix, prime

%o 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

%Y Cf. A350932, A350955.

%K nonn,hard,more

%O 0,2

%A _N. J. A. Sloane_ and _Stefano Spezia_, Jan 28 2022

%E a(9) from _Alois P. Heinz_, Jan 28 2022

%E a(10)-a(12) from _Lucas A. Brown_, Aug 31 2022