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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.
6
1, 1, -3, 8, -21, -12167, -1708047, -116428560, -33081320935, -1098860747703, -579469550006151
OFFSET
0,3
EXAMPLE
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]
MATHEMATICA
a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]
CROSSREFS
Cf. A374341 (maximal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
Sequence in context: A353424 A156291 A111136 * A348636 A063937 A363593
KEYWORD
sign,hard,more
AUTHOR
Stefano Spezia, Jul 05 2024
STATUS
approved