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

Author

Stefano Spezia, Jul 05 2024

Keywords

• sign
• hard
• more

Examples

			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]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A071078, A374240.

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

Programs

Mathematica

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