A374342 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.

1, 1, 3, 15, 259, 12167, 1708047, 157042600, 33081320935, 3336975844504, 579469550006151

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Wikipedia, Toeplitz Matrix.

Formula

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

Example

a(5) = 12167:
  [1, 2, 7, 3, 5]
  [2, 1, 2, 7, 3]
  [7, 2, 1, 2, 7]
  [3, 7, 2, 1, 2]
  [5, 3, 7, 2, 1]

Mathematica

a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Prime[Range[n-1]]], i]]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]

Crossrefs

Cf. A071078, A374241.

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

Sequence in context: A250405 A051179 A374341 * A122591 A326263 A120607

Adjacent sequences: A374339 A374340 A374341 * A374343 A374344 A374345

Keyword

nonn,hard,more

Author

Stefano Spezia, Jul 05 2024

Status

approved