A374341 a(n) is the maximal 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, 1608, 1582152, 157042600, 11778545664, 3336975844504, 440384712302421

Offset

0,3

Links

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

Wikipedia, Toeplitz Matrix.

Example

a(5) = 1608:
  [1, 7, 2, 3, 5]
  [7, 1, 7, 2, 3]
  [2, 7, 1, 7, 2]
  [3, 2, 7, 1, 7]
  [5, 3, 2, 7, 1]

Mathematica

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

Crossrefs

Cf. A071078, A374240.

Cf. A374340 (minimal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Sequence in context: A050474 A250405 A051179 * A374342 A122591 A326263

Adjacent sequences: A374338 A374339 A374340 * A374342 A374343 A374344

Keyword

sign,hard,more

Author

Stefano Spezia, Jul 05 2024

Status

approved