A374067 - OEIS

A374067

a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th prime or 1 if i = j.

1, 1, 5, 42, 753, 22969, 1226225, 98413280, 11551199289, 1828335971613, 379823112871605, 102232301626742202, 34359550765856135217, 14289766516805617273497, 7224166042347461997365713, 4334493536305030883929928032, 3046742350470292308074313518937, 2492781304663024301187012794633153

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OFFSET

0,3

COMMENTS

Conjecture: a(n) is the minimal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal. - Stefano Spezia, Jul 08 2024

LINKS

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

EXAMPLE

a(4) = 753:

[1, 2, 3, 5]

[2, 1, 2, 3]

[3, 2, 1, 2]

[5, 3, 2, 1]

MATHEMATICA

a[n_]:=Permanent[Table[ If[i == j, 1, 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, 1, prime(abs(i-j))))); \\ Michel Marcus, Jun 27 2024