A374340 a(n) is the minimal 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, 8, -21, -12167, -1708047, -116428560, -33081320935, -1098860747703, -579469550006151

Offset: 0

Author

Stefano Spezia, Jul 05 2024

Keywords

• sign
• hard
• more

Examples

			a(5) = -12167:
  [1, 2, 7, 3, 5]
  [2, 1, 2, 7, 3]
  [7, 2, 1, 2, 7]
  [3, 7, 2, 1, 2]
  [5, 3, 7, 2, 1]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A071078, A374239.

Cf. A374341 (maximal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

Mathematica

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