A374068 - OEIS

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A374068

a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th prime or 0 if i = j.

1, 0, 4, 24, 529, 16100, 919037, 75568846, 9196890092, 1491628025318, 317579623173729, 86997150829931700, 29703399282858184713, 12512837775355494800500, 6397110844644502402189404, 3875565057688532269985283868, 2747710211567246171588232074225, 2265312860218073375019946448731300

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OFFSET

0,3

COMMENTS

Conjecture: a(n) is the minimal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal. - Stefano Spezia, Jul 06 2024

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

a(4) = 529:

[0, 2, 3, 5]

[2, 0, 2, 3]

[3, 2, 0, 2]

[5, 3, 2, 0]

MATHEMATICA

a[n_]:=Permanent[Table[If[i == j, 0, Prime[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1}, Array[a, 17]]

PROG

(PARI) a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 0, prime(abs(i-j))))); \\ Michel Marcus, Jun 28 2024