A374386 a(n) is the minimal 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, 24, -324, -15164, -1453072, -161765904, -37905894000, -1376219654680, -718058901423168, -163742479201610036

Offset: 0

Author

Stefano Spezia, Jul 07 2024

Keywords

• sign
• 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, A374340.

Cf. A374387 (maximal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).

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

Programs

Mathematica

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

Extensions

a(11) from Giorgos Kalogeropoulos, Jul 10 2024