A374068 - OEIS

%I #18 Jul 06 2024 19:48:22

%S 1,0,4,24,529,16100,919037,75568846,9196890092,1491628025318,

%T 317579623173729,86997150829931700,29703399282858184713,

%U 12512837775355494800500,6397110844644502402189404,3875565057688532269985283868,2747710211567246171588232074225,2265312860218073375019946448731300

%N 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.

%C 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

%e a(4) = 529:

%e   [0, 2, 3, 5]

%e   [2, 0, 2, 3]

%e   [3, 2, 0, 2]

%e   [5, 3, 2, 0]

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

%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 0, prime(abs(i-j))))); \\ _Michel Marcus_, Jun 28 2024

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

%Y Cf. A374067, A374069, A374070, A374071.

%K nonn

%O 0,3

%A _Stefano Spezia_, Jun 27 2024