A369949 - OEIS

%I #15 Feb 12 2024 12:41:43

%S 1,1,3,59,2459,174063,19141721

%N a(n) is the number of distinct values of the determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.

%t a[n_] := CountDistinct[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]

%o (PARI) a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matdet(matrix(n, n, i, j, prime(p[i+j-1]))));); #Set(list); \\ _Michel Marcus_, Feb 08 2024

%o (Python)

%o from itertools import permutations

%o from sympy import primerange, prime, Matrix

%o def A369949(n): return len({Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(primerange(prime((n<<1)-1)+1))}) if n else 1 # _Chai Wah Wu_, Feb 12 2024

%Y Cf. A024356, A369946, A369947, A350933.

%K nonn,hard,more

%O 0,3

%A _Stefano Spezia_, Feb 06 2024

%E a(6) from _Michel Marcus_, Feb 08 2024