A369832 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.

1, 1, 2, 6, 24, 116, 717, 5033, 40301, 362845

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Wikipedia, Toeplitz Matrix.

Formula

a(n) <= A000142(n).

Mathematica

a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a, 9]]

Prog

(Python)
from itertools import permutations
from sympy import primerange, prime, Matrix
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

Crossrefs

Cf. A000142, A348891, A350955, A350956.

Cf. A369830, A369831, A369833, A369834, A369835.

Sequence in context: A221988 A329788 A177518 * A319027 A228397 A164871

Adjacent sequences: A369828 A369830 A369831 * A369833 A369834 A369835

Keyword

nonn,hard,more

Author

Stefano Spezia, Feb 03 2024

Status

approved