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A374341 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.

%I A374341 #11 Jul 11 2024 01:48:10
%S A374341 1,1,-3,15,259,1608,1582152,157042600,11778545664,3336975844504,
%T A374341 440384712302421
%N A374341 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 A374341 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374341 a(5) = 1608:
%e A374341   [1, 7, 2, 3, 5]
%e A374341   [7, 1, 7, 2, 3]
%e A374341   [2, 7, 1, 7, 2]
%e A374341   [3, 2, 7, 1, 7]
%e A374341   [5, 3, 2, 7, 1]
%t A374341 a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y A374341 Cf. A071078, A374240.
%Y A374341 Cf. A374340 (minimal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
%K A374341 sign,hard,more
%O A374341 0,3
%A A374341 _Stefano Spezia_, Jul 05 2024