A369949 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.

1, 1, 3, 59, 2459, 174063, 19141721

Offset: 0

Author

Stefano Spezia, Feb 06 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Hankel matrix.

Crossrefs

Cf. A024356, A369946, A369947, A350933.

Programs

Mathematica

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]]

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

Python

from itertools import permutations
from sympy import primerange, prime, Matrix
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

Extensions

a(6) from Michel Marcus, Feb 08 2024