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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.
5

%I #11 Jul 10 2024 13:43:03

%S 1,0,-4,24,-324,-15164,-1453072,-161765904,-37905894000,

%T -1376219654680,-718058901423168,-163742479201610036

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

%e a(5) = -15164:

%e [0, 2, 7, 3, 5]

%e [2, 0, 2, 7, 3]

%e [7, 2, 0, 2, 7]

%e [3, 7, 2, 0, 2]

%e [5, 3, 7, 2, 0]

%t a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

%Y Cf. A071079, A374340.

%Y Cf. A374387 (maximal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).

%Y Cf. A374068 (minimal permanent), A374390 (maximal permanent).

%K sign,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 07 2024

%E a(11) from _Giorgos Kalogeropoulos_, Jul 10 2024