A374343 - OEIS

%I #9 Jul 08 2024 09:01:43

%S 1,1,3,8,7,32,81,504,327,95

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

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

%e a(5) = 32:

%e   [1, 3, 2, 5, 7]

%e   [3, 1, 3, 2, 5]

%e   [2, 3, 1, 3, 2]

%e   [5, 2, 3, 1, 3]

%e   [7, 5, 2, 3, 1]

%t a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}],Positive]]; Join[{1},Array[a,10]]

%Y Cf. A071078, A374242.

%Y Cf. A374340 (minimal), A374341 (maximal), A374342 (maximal absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 05 2024