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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.
5
1, 1, 3, 8, 7, 32, 81, 504, 327, 95
OFFSET
0,3
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. A374340 (minimal), A374341 (maximal), A374342 (maximal absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
Sequence in context: A122237 A307162 A233418 * A280581 A278755 A016625
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 05 2024
STATUS
approved