A374388 a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

1, 0, 4, 36, 324, 15164, 2287607, 162104000, 37905894000, 4059346088384, 718058901423168, 221630954408019520

Offset: 0

Author

Stefano Spezia, Jul 07 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 15164:
  [0, 2, 7, 3, 5]
  [2, 0, 2, 7, 3]
  [7, 2, 0, 2, 7]
  [3, 7, 2, 0, 2]
  [5, 3, 7, 2, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A071079, A374342.

Cf. A374386 (minimal), A374387 (maximal), A374389 (minimal nonzero absolute value).

Cf. A374068 (minimal permanent), A374390 (maximal permanent).

Programs

Mathematica

a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

Formula

a(n) = max(abs(A374386(n)), A374387(n)).

Extensions

a(11) from Giorgos Kalogeropoulos, Jul 12 2024