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A350939
Minimal permanent of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
6
1, 2, 19, 496, 29609, 3009106, 498206489
OFFSET
0,2
COMMENTS
For n X n Hankel matrices the same minimal permanents appear.
EXAMPLE
a(2) = 19:
2 3
5 2
a(3) = 496:
2 3 7
5 2 3
11 5 2
MATHEMATICA
a[n_] := Min[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]] (* Stefano Spezia, Feb 06 2024 *)
PROG
(Python)
from itertools import permutations
from sympy import Matrix, prime
def A350939(n): return 1 if n == 0 else min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(prime(i) for i in range(1, 2*n))) # Chai Wah Wu, Jan 27 2022
(PARI) a(n) = my(v=[1..2*n-1], m=+oo, d); forperm(v, p, d = matpermanent(matrix(n, n, i, j, prime(p[i+j-1]))); if (d<m, m = d)); m; \\ Michel Marcus, Feb 08 2024
CROSSREFS
Sequence in context: A353290 A332967 A120420 * A239674 A306457 A158099
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jan 26 2022
EXTENSIONS
a(5) from Alois P. Heinz, Jan 26 2022
a(6) from Lucas A. Brown, Sep 05 2022
STATUS
approved