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A374342 a(n) is the maximal absolute value of the 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 A374342 #11 Jul 08 2024 08:39:05
%S A374342 1,1,3,15,259,12167,1708047,157042600,33081320935,3336975844504,
%T A374342 579469550006151
%N A374342 a(n) is the maximal absolute value of the 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 A374342 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F A374342 a(n) = max(abs(A374340(n)),A374341(n)).
%e A374342 a(5) = 12167:
%e A374342   [1, 2, 7, 3, 5]
%e A374342   [2, 1, 2, 7, 3]
%e A374342   [7, 2, 1, 2, 7]
%e A374342   [3, 7, 2, 1, 2]
%e A374342   [5, 3, 7, 2, 1]
%t A374342 a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y A374342 Cf. A071078, A374241.
%Y A374342 Cf. A374340 (minimal), A374341 (maximal), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
%K A374342 nonn,hard,more
%O A374342 0,3
%A A374342 _Stefano Spezia_, Jul 05 2024