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A374343 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.

%I A374343 #9 Jul 08 2024 09:01:43
%S A374343 1,1,3,8,7,32,81,504,327,95
%N A374343 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 A374343 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374343 a(5) = 32:
%e A374343   [1, 3, 2, 5, 7]
%e A374343   [3, 1, 3, 2, 5]
%e A374343   [2, 3, 1, 3, 2]
%e A374343   [5, 2, 3, 1, 3]
%e A374343   [7, 5, 2, 3, 1]
%t A374343 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 A374343 Cf. A071078, A374242.
%Y A374343 Cf. A374340 (minimal), A374341 (maximal), A374342 (maximal absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
%K A374343 nonn,hard,more
%O A374343 0,3
%A A374343 _Stefano Spezia_, Jul 05 2024