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A374342
a(n) is the maximal absolute value of the 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, 15, 259, 12167, 1708047, 157042600, 33081320935, 3336975844504, 579469550006151
OFFSET
0,3
FORMULA
a(n) = max(abs(A374340(n)),A374341(n)).
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_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Prime[Range[n-1]]], i]]]]], {i, (n-1)!}]]; Join[{1}, Array[a, 10]]
CROSSREFS
Cf. A374340 (minimal), A374341 (maximal), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).
Sequence in context: A250405 A051179 A374341 * A122591 A326263 A120607
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 05 2024
STATUS
approved