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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.
4
1, 1, 9, 107, 2609, 98089, 5564610, 438180102, 46399705928, 6279673881161, 1060663766284535, 222840745939132105, 56798048066468972011, 17364018690978269373950, 6261448805827102522607660, 2624315396531837995006160020, 1263427401352418949898456181999, 693487403043958170112254851399169
OFFSET
0,3
EXAMPLE
a(4) = 2609:
[1, 2, 3, 5]
[4, 1, 2, 3]
[6, 4, 1, 2]
[8, 6, 4, 1]
MAPLE
P, C:= selectremove(isprime, [$2..100]):
f:= proc(n) local i; uses LinearAlgebra;
Permanent(ToeplitzMatrix([seq(C[i], i=n-1..1, -1), 1, seq(P[i], i=1..n-1)]))
end proc:
map(f, [$0..20]); # Robert Israel, Jun 27 2024
MATHEMATICA
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]]
CROSSREFS
Cf. A071082 (determinant).
Sequence in context: A316145 A365032 A039619 * A249048 A080505 A104224
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jun 27 2024
STATUS
approved