%I #11 Feb 11 2024 11:21:10
%S 1,1,2,6,24,116,717,5033,40301,362845
%N a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%F a(n) <= A000142(n).
%t a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
%o (Python)
%o from itertools import permutations
%o from sympy import primerange, prime, Matrix
%o def A369832(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(primerange(prime(n)+1))}) if n else 1 # _Chai Wah Wu_, Feb 11 2024
%Y Cf. A000142, A348891, A350955, A350956.
%Y Cf. A369830, A369831, A369833, A369834, A369835.
%K nonn,hard,more
%O 0,3
%A _Stefano Spezia_, Feb 03 2024