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

2,1

Comments

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

Links

Table of n, a(n) for n=2..9.

Wikipedia, Toeplitz Matrix.

Example

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]

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]

Crossrefs

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

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

Sequence in context: A099582 A295093 A211142 * A272735 A295547 A270451

Adjacent sequences: A374386 A374387 A374388 * A374390 A374391 A374392

Keyword

nonn,hard,more

Author

Stefano Spezia, Jul 07 2024

Status

approved