login
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.
6

%I #11 Jul 08 2024 08:39:05

%S 1,1,3,15,259,12167,1708047,157042600,33081320935,3336975844504,

%T 579469550006151

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

%F a(n) = max(abs(A374340(n)),A374341(n)).

%e a(5) = 12167:

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

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

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

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

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

%t 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 Cf. A071078, A374241.

%Y Cf. A374340 (minimal), A374341 (maximal), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 05 2024