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

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

Crossrefs

Cf. A071079 (determinant), A085807, A306457, A318173.

Cf. A374067, A374069, A374070, A374071.

Sequence in context: A009535 A139096 A111425 * A013100 A013061 A071302

Adjacent sequences: A374065 A374066 A374067 * A374069 A374070 A374071

Keyword

nonn,new

Author

Stefano Spezia, Jun 27 2024

Status

approved