A374343 a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

1, 1, 3, 8, 7, 32, 81, 504, 327, 95

Offset: 0

Author

Stefano Spezia, Jul 05 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 32:
  [1, 3, 2, 5, 7]
  [3, 1, 3, 2, 5]
  [2, 3, 1, 3, 2]
  [5, 2, 3, 1, 3]
  [7, 5, 2, 3, 1]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A071078, A374242.

Cf. A374340 (minimal), A374341 (maximal), A374342 (maximal absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

Mathematica

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