A350956 - OEIS

A350956

Maximal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 2, 5, 64, 1107, 160160, 5713367, 889747443, 62837596341, 11671262491586, 3090090680653053, 635672008069583520, 278356729040728193703

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

Lucas A. Brown, A348891+A350955+6.py

Wikipedia, Toeplitz Matrix

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

Adjacent sequences: A350953 A350954 A350955 * A350957 A350958 A350959

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