A374389 - OEIS

%I #5 Jul 07 2024 13:48:57

%S 4,24,116,192,1079,664,720,216

%N a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

%C The offset is 2 because for n = 1 the unique symmetric Toeplitz matrix is singular.

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

%e a(5) = 192:

%e   [0, 5, 3, 2, 7]

%e   [5, 0, 5, 3, 2]

%e   [3, 5, 0, 5, 3]

%e   [2, 3, 5, 0, 5]

%e   [7, 2, 3, 5, 0]

%t a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,8,2]

%Y Cf. A374386 (minimal), A374387 (maximal), A374388 (maximal absolute value).

%Y Cf. A374068 (minimal permanent), A374390 (maximal permanent).

%K nonn,hard,more

%O 2,1

%A _Stefano Spezia_, Jul 07 2024