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A350956
Maximal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.
9
1, 2, 5, 64, 1107, 160160, 5713367, 889747443, 62837596341, 11671262491586, 3090090680653053, 635672008069583520, 278356729040728193703
OFFSET
0,2
EXAMPLE
a(3) = 64:
[5 2 3]
[2 5 2]
[3 2 5]
a(4) = 1107:
[3 2 7 5]
[2 3 2 7]
[7 2 3 2]
[5 7 2 3]
a(5) = 160160:
[ 5 11 2 3 7]
[11 5 11 2 3]
[ 2 11 5 11 2]
[ 3 2 11 5 11]
[ 7 3 2 11 5]
PROG
(Python)
from itertools import permutations
from sympy import Matrix, prime
def A350956(n): return max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1, n+1))) # Chai Wah Wu, Jan 27 2022
CROSSREFS
Cf. A350933, A350955 (minimal).
Sequence in context: A027667 A076630 A270389 * A086560 A305292 A268211
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jan 27 2022
EXTENSIONS
a(9) from Alois P. Heinz, Jan 27 2022
a(10)-a(12) from Lucas A. Brown, Aug 29 2022
STATUS
approved