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a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.
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%I #11 Jul 11 2024 01:48:10

%S 1,1,-3,15,259,1608,1582152,157042600,11778545664,3336975844504,

%T 440384712302421

%N a(n) is the maximal 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.

%e a(5) = 1608:

%e [1, 7, 2, 3, 5]

%e [7, 1, 7, 2, 3]

%e [2, 7, 1, 7, 2]

%e [3, 2, 7, 1, 7]

%e [5, 3, 2, 7, 1]

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

%Y Cf. A071078, A374240.

%Y Cf. A374340 (minimal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

%K sign,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 05 2024