A374386 - OEIS

A374386

a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

1, 0, -4, 24, -324, -15164, -1453072, -161765904, -37905894000, -1376219654680, -718058901423168, -163742479201610036

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OFFSET

0,3

LINKS

EXAMPLE

a(5) = -15164:

[0, 2, 7, 3, 5]

[2, 0, 2, 7, 3]

[7, 2, 0, 2, 7]

[3, 7, 2, 0, 2]

[5, 3, 7, 2, 0]

MATHEMATICA

a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0}, Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]

CROSSREFS

Cf. A374387 (maximal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).

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

KEYWORD

sign,hard,more

AUTHOR

EXTENSIONS

a(11) from Giorgos Kalogeropoulos, Jul 10 2024

STATUS

approved