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%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