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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.
5
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.
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
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 07 2024
STATUS
approved