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A073364
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Number of permutations p of (1,2,3,...,n) such that k+p(k) is prime for 1<=k<=n.
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12
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1, 1, 1, 4, 1, 9, 4, 36, 36, 676, 400, 9216, 3600, 44100, 36100, 1223236, 583696, 14130081, 5461569, 158180929, 96275344, 5486661184, 2454013444, 179677645456, 108938283364, 5446753133584, 4551557699844, 280114147765321, 125264064932449, 9967796169000201
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OFFSET
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1,4
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COMMENTS
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a(n)=permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether i+j is prime or composite respectively. - T. D. Noe, Oct 16 2007
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LINKS
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FORMULA
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MATHEMATICA
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am[n_] := Permanent[Array[Boole[PrimeQ[2 #1 + 2 #2 - 1]]&, {n, n}]];
ap[n_] := Permanent[Array[Boole[PrimeQ[2 #1 + 2 #2 + 1]]&, {n, n}]];
a[n_] := If[n == 1, 1, If[EvenQ[n], am[n/2]^2, ap[(n-1)/2]^2]];
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PROG
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(PARI) a(n)=sum(k=1, n!, n==sum(i=1, n, isprime(i+component(numtoperm(n, k), i))))
(PARI) a(n)={matpermanent(matrix(n, n, i, j, isprime(i + j)))} \\ Andrew Howroyd, Nov 03 2018
(Haskell)
a073364 n = length $ filter (all isprime)
$ map (zipWith (+) [1..n]) (permutations [1..n])
where isprime n = a010051 n == 1 -- cf. A010051
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(10) from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 14 2004
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STATUS
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approved
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