cp's OEIS Frontend

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.

%I A374067 #16 Jul 11 2024 01:48:07
%S A374067 1,1,5,42,753,22969,1226225,98413280,11551199289,1828335971613,
%T A374067 379823112871605,102232301626742202,34359550765856135217,
%U A374067 14289766516805617273497,7224166042347461997365713,4334493536305030883929928032,3046742350470292308074313518937,2492781304663024301187012794633153
%N 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.
%C A374067 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
%e A374067 a(4) = 753:
%e A374067   [1, 2, 3, 5]
%e A374067   [2, 1, 2, 3]
%e A374067   [3, 2, 1, 2]
%e A374067   [5, 3, 2, 1]
%t A374067 a[n_]:=Permanent[Table[ If[i == j, 1, Prime[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a, 17]]
%o A374067 (PARI) a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, prime(abs(i-j))))); \\ _Michel Marcus_, Jun 27 2024
%Y A374067 Cf. A071078 (determinant), A306457, A318173.
%Y A374067 Cf. A374068, A374069, A374070, A374071.
%K A374067 nonn
%O A374067 0,3
%A A374067 _Stefano Spezia_, Jun 27 2024