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

0,3

Links

Table of n, a(n) for n=0..9.

Wikipedia, Toeplitz Matrix.

Example

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]

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]]

Crossrefs

Cf. A071078, A374242.

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

Sequence in context: A122237 A307162 A233418 * A280581 A278755 A016625

Adjacent sequences: A374340 A374341 A374342 * A374345 A374346 A374347

Keyword

nonn,hard,more,new

Author

Stefano Spezia, Jul 05 2024

Status

approved