A374389 a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

4, 24, 116, 192, 1079, 664, 720, 216

Offset: 2

Author

Stefano Spezia, Jul 07 2024

Keywords

• nonn
• hard
• more

Comments

The offset is 2 because for n = 1 the unique symmetric Toeplitz matrix is singular.

Examples

			a(5) = 192:
  [0, 5, 3, 2, 7]
  [5, 0, 5, 3, 2]
  [3, 5, 0, 5, 3]
  [2, 3, 5, 0, 5]
  [7, 2, 3, 5, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A374386 (minimal), A374387 (maximal), A374388 (maximal absolute value).

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

Programs

Mathematica

a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,8,2]