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A374340 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

%I A374340 #12 Jul 11 2024 01:48:03
%S A374340 1,1,-3,8,-21,-12167,-1708047,-116428560,-33081320935,-1098860747703,
%T A374340 -579469550006151
%N A374340 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.
%H A374340 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374340 a(5) = -12167:
%e A374340   [1, 2, 7, 3, 5]
%e A374340   [2, 1, 2, 7, 3]
%e A374340   [7, 2, 1, 2, 7]
%e A374340   [3, 7, 2, 1, 2]
%e A374340   [5, 3, 7, 2, 1]
%t A374340 a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y A374340 Cf. A071078, A374239.
%Y A374340 Cf. A374341 (maximal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
%K A374340 sign,hard,more
%O A374340 0,3
%A A374340 _Stefano Spezia_, Jul 05 2024