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%I A374386 #11 Jul 10 2024 13:43:03
%S A374386 1,0,-4,24,-324,-15164,-1453072,-161765904,-37905894000,
%T A374386 -1376219654680,-718058901423168,-163742479201610036
%N A374386 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.
%H A374386 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374386 a(5) = -15164:
%e A374386   [0, 2, 7, 3, 5]
%e A374386   [2, 0, 2, 7, 3]
%e A374386   [7, 2, 0, 2, 7]
%e A374386   [3, 7, 2, 0, 2]
%e A374386   [5, 3, 7, 2, 0]
%t A374386 a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y A374386 Cf. A071079, A374340.
%Y A374386 Cf. A374387 (maximal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).
%Y A374386 Cf. A374068 (minimal permanent), A374390 (maximal permanent).
%K A374386 sign,hard,more
%O A374386 0,3
%A A374386 _Stefano Spezia_, Jul 07 2024
%E A374386 a(11) from _Giorgos Kalogeropoulos_, Jul 10 2024

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