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A374071 a(n) is the permanent of the Toeplitz matrix of order n whose element (i,j) equals the (i-j)-th composite number if i > j, (j-i)-th prime number if i < j, or 1 if i = j.

%I A374071 #11 Jun 30 2024 16:28:30
%S A374071 1,1,9,107,2609,98089,5564610,438180102,46399705928,6279673881161,
%T A374071 1060663766284535,222840745939132105,56798048066468972011,
%U A374071 17364018690978269373950,6261448805827102522607660,2624315396531837995006160020,1263427401352418949898456181999,693487403043958170112254851399169
%N A374071 a(n) is the permanent of the Toeplitz matrix of order n whose element (i,j) equals the (i-j)-th composite number if i > j, (j-i)-th prime number if i < j, or 1 if i = j.
%e A374071 a(4) = 2609:
%e A374071   [1, 2, 3, 5]
%e A374071   [4, 1, 2, 3]
%e A374071   [6, 4, 1, 2]
%e A374071   [8, 6, 4, 1]
%p A374071 P,C:= selectremove(isprime,[$2..100]):
%p A374071 f:= proc(n) local i; uses LinearAlgebra;
%p A374071   Permanent(ToeplitzMatrix([seq(C[i],i=n-1..1,-1),1,seq(P[i],i=1..n-1)]))
%p A374071 end proc:
%p A374071 map(f, [$0..20]); # _Robert Israel_, Jun 27 2024
%t A374071 Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; a[n_]:= Permanent[Table[If[i == j, 1, If[i > j, Composite[i - j], Prime[j - i]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a, 17]]
%Y A374071 Cf. A071082 (determinant).
%Y A374071 Cf. A374067, A374068, A374069, A374070.
%K A374071 nonn
%O A374071 0,3
%A A374071 _Stefano Spezia_, Jun 27 2024